Cheese like slime on potato, but no pinkness I had some potatoes in the back of a cupboard, and one solitary potato has sort of disintegrated into a cheesy yellow slime.

The skin looks mostly intact, and the slime is sticky exactly like melted cheese. I looked up potato slime, and the only similar ailment was pink slime, but there's no pink here.
They were not old enough for any other signs of rot.
I've washed the other potatoes, and will monitor them.
What happened to that one potato.
It rotted - that's about all you can say from this. Most likely a bacterial rot rather than a fungal rot. If you bought them recently, it was probably already rotting.
This is a form of soft rot, which is a common disease of potatoes world-wide, and can even destroy whole crops in the field. There are a range of bacteria that cause these rots, but Pectobacterium is a common genus for this form of rot.