The council is consulting on shutting Bodlondeb in Penparcau, Aberystwyth, with the loss of 33 jobs.
A report said residents would have to move to other homes - potentially long distances away.
The council previously said the building would need significant investment to continue operating.
It added it appreciated Bodlondeb was "very important to the people of Aberystwyth and beyond and this is a very sensitive matter for all involved".
GMB and Unison, which represent staff at Bodlondeb, said the closure came with "no plan for improving or securing the long term provision of care for the elderly within our community".
A consultation is due to run until 25 September and a public meeting is being held on 17 July at Llwyn yr Eos primary school from 19:00 BST.
Unison branch secretary Owain Davies said: "It is simply the closure of a well-loved and valued home, in order to help balance a budget that has been cut to the bone - and now into the bone.
"At a time when everyone is acknowledging that demands on social care for the elderly are rising, it is absurd for Ceredigion Council to be proposing the closure of its sole remaining residential home in its most populated town, especially as the closure comes with no plans or details as to how the increasing demands are going to be met with less capacity and less facilities."
Unison added it recognised the financial difficulties facing the council, but said this proposal was "an inappropriate and inadequate response".
Althea Phillips, regional organiser for the GMB, said: "All of the staff at the home are dedicated and hard-working and it is their efforts over the years that has kept Bodlondeb in high regard in the community, they deserve to be treated better than this."
A report to the council said the Bodlondeb home has been operating at a loss of nearly Â£400,000 per year - more than Â£7,600 per week.
The council said there were empty spaces in care homes across the county which reflects the "changing nature of care requirements".
A spokeswoman added the council had been meeting regularly with union representatives and Bodlondeb staff.

The search was launched after the coastguard received reports from an individual claiming to be in difficulty off the coast of County Down.
Two RNLI boats and a coastguard helicopter from Scotland were launched to assist in the search.
The kayaker was reported to be near Mew Island, one of the Copeland Islands near Donaghadee.
A coastguard spokesman said it received several calls from a person claiming to be in difficulty.
However, the alarm was declared to be a hoax following a thorough search.

Prop Mako Vunipola, 25, and 23-year-old brother Billy, started their careers at Thornbury Rugby Club.
Both have become England regulars since joining Saracens, with Mako winning 29 international caps and Billy 23.
They were both junior members at the club on the outskirts of Bristol in South Gloucestershire.
Roy Black, who was chairman of Thornbury RFC at the time, said they were "big lads" when they were 11 or 12 and caused the opposition "a lot of problems"
"If you saw them in Thornbury and they were walking to the club or to school they'd always have a rugby ball in their hand and throwing it from one side of the road to the other over the traffic," he said.
Mr Black also recounted the time when Lloyd Spacey, their PE teacher at nearby Castle School, was knocked to the ground by Mako after asking him "did he play rugby".
"Mako grunted 'yes', so Lloyd picked up a tackle bag and Mako ran straight through him when he was about 13," Mr Black said.

Two men took £200 from the shop at Rosskeen Park at 04:00 GMT on Thursday before making off in the stolen car.
Police said the black Citroen C1 was stolen from the Shearwater area.
Shop owner Pat O'Reilly told BBC Radio Foyle: "This will cost us thousands but we'll pick ourselves up and get back to it though."
He added: "Shelving, freezers and shutters have been badly damaged.
"We have put so much money in to this place. The shop was going well too.
"We are going to be closed for a while and staff still have to get paid. This is just a nightmare."
A council's proposal to shut a Ceredigion care home comes with "no plan" for care provision in the area, unions have said.
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The coastguard has called off a search for a kayaker after it declared the alarm an "elaborate hoax".
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Two international rugby stars have returned to their home club to help coach an under-10s team and to watch the first XV in action.
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A Londonderry shop owner has said the repair bill for damage caused to his shop, after a stolen car was rammed into it, will be around £10,000.