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I remember seeing in [the thread
before](https://japanese.stackexchange.com/questions/3361/%E5%A4%AA%E3%81%A3%E3%81%A6%E3%82%8B%E7%8C%AB-
vs-%E5%A4%AA%E3%81%A3%E3%81%9F%E7%8C%AB/3364#3364.) that there was no
difference between ている and た. So then what would be the difference between the
usage of them in these sentences below?

>   * 最後に立っていたものが勝者だ
>   * 最後に立っているものが勝者だ
>   * 最後に立ったものが勝者だ
>

All the above are from using google search with the first two being the most
common and the third being the least with only two hits with the words
`最後に立ったものが`.
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relative-clauses
What is the difference between using ている、ていた、た in relative clauses?
For general explanations, it's better to see the posts you and Darius (in his
comment) mentioned. Here I focus on specific issues.

**Summary:**

  * 最後に立っていたものが勝者だ  
_Who was standing at the end {is / will be} the winner._  
or _Who {is / will be} standing at the end {becomes / will become} the
winner._ .........(*1)

  * 最後に立っているものが勝者だ  
_The winner {is / will be} who {is / will be} standing at the end._  
or _Who {is / will be} standing at the end equals to the winner._
.........(*2)

  * 最後に立ったものが勝者だ  
_Who stood up last {is / will be} the winner._

**Discussions:**

There are two factors you should take care of.

First, the verb `立つ` means " _to stand **up_** ", not " _to stand_ ". The
"standing" (`立っている`) sense is only possible as its result. That's why your
third example is the odd one out. What I imagined was a chicken game sitting
on hot chair as long as possible.

Your first and second examples both could translate the English sentence, "The
last one standing is the winner." So, what's the difference? It's very subtle,
but put shortly, the first one is what you'd typically say when you think: "If
someone's standing alone, then he/she wins.", while the second one is
typically used when you think: "I'll know who's the winner by seeing someone's
standing alone".

The difference eventually comes from that Japanese "past tense particle" `-た`
doesn't exactly means what _happened_ in past, but what _was confirmed_ in
past. In the first sentence, you first judge there's only one person standing,
and in the next step, you judge that person wins. Thus I chose verb _become_
in my translation (*1). On the other hand, the second one insists that the two
judgments are possible in a overlapped time range. Usually the interpretation
has no problem, like `立っているものが勝者だ` sounds perfectly natural, but in this
specific case, `最後に` "at the end" inevitably evokes the feeling that the only
timing to judge the "standing" is the very moment a match ends, therefore you
couldn't shake off some unnatural ring except you're telling a solid,
universal fact (*2).
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>   * 最後に立っていたものが勝者だ
>

The last person who **was** (still) standing is the winner

>   * 最後に立っているものが勝者だ
>

The last person who **is** (still) standing is the winner

>   * 最後に立ったものが勝者だ
>

The person who stands up last is the winner

The third one is uncommon because there aren't many competition where you try
to not stand up.
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answer
Well, as with any sentences that don't have a large number of adjuncts or
context limiting their meaning, there are many interpretations.

* * *

> 最後に立っ **ていた** ものが勝者 _だ_

  1. **Matrix time** : present  
**Subordinate time** : past

> ("Who is the winner?")  
>  "The last person who **was** standing _is_ the winner."

That is, the person who was (before time of speech) standing up last (and may
or may not be standing at time of speech) is the winner.

  2. **Matrix time** : future  
**Subordinate time** : past or relative past

> "The last person who **was** standing ( _will be_ / _is_ ) the winner."

That is, either:

    * " **was** " = past: the person who was (before the time of speech) standing up last (and may or may not be standing at the time of speech) will be the winner.
    * " **was** " = relative past: the person who was (before the reference time) standing up last (and may or may not be standing at the reference time) will be the winner.

(As for the English gloss, this sentence suggests the past interpretation as
opposed to the relative past interpretation at first glance, I think. But,
with enough context: "In this game, people sit up and down in order, and then
a bell randomly rings. When that happens, the person who was standing up last
will be the winner.", the relative past interpretation works fine in English
as well.)

For both interpretations, in Japanese and the English glosses, whether the
person is still standing up or not is not specified, though there is probably
a slight suggestion of "no longer standing" (since you would use 「立っている」/"is
standing" otherwise, after all).

* * *

> 最後に立っ **ている** ものが勝者 _だ_

  1. **Matrix time** : present  
**Subordinate time** : present

> ("Who is the winner?")  
>  "The last person who **is** standing _is_ the winner."

That is, the person who is (at time of speech) standing is the winner.

Honestly, interpreting this sentence as occurring in present time is slightly
weird, since you'd probably just say 「立っている人が勝者だ」 "The standing person is the
winner.".

  2. **Matrix time** : future  
**Subordinate time** : present or relative present

> "The last person who **is** standing ( _will be_ / _is_ ) the winner."

That is, either:

    * " **is** " = present: the person who is (at time of speech) standing up last is the winner.
    * " **is** " = relative present: the person who is (at reference time) standing up last is the winner.

Again, the present is somewhat pragmatically weird, since you would normally
not use 「最後に」 "last" -- that means this sentence would probably have the
subordinate clause interpreted in the relative present.

* * *

> 最後に立っ **た** ものが勝者 _だ_

  1. **Matrix time** : present  
**Subordinate time** : past

> ("Who is the winner?")  
>  "The last person who **stood up** _is_ the winner."

That is, the person who (before the time of speech) stood up last (and may or
may not be standing at time of speech) is the winner.

  2. **Matrix time** : future  
**Subordinate time** : past or relative past

> "The last person who **stood up** ( _will be_ / _is_ ) the winner."

That is, either:

    * " **stood up** " = past: The person who (before the time of speech) stood up last (and may or may not be standing at the time of speech) will be the winner.
    * " **stood up** " = relative past: The person who (before the reference time) stood up last (and may or may not be standing at the reference time) will be the winner.

* * *

Finally, to address the core of your confusion, **「た」 cannot be interpreted as
「ている」 here** (which is hopefully clear due to the different glosses provided).

The reason for this is because (as further explained in the thread I linked in
the comments), the actor (namely, the person who stood up) is explicitly
mentioned in the sentence, which prevents the stative reading of 「た」. With a
different head, like 「立った状態」, 「立った」 can be interpreted as 「立っている」.
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answer