I’m taking care of my neighbour’s animals-- two cats and a smelly dog-- and one of the cats left a nasty deposit on top of one of their couches, which I discovered by leaning into it, unfortunately.
This slime was mostly clear with some bits of grue in it, and I really did not appreciate my mode of discovery!
Three questions: what the hell was it?
Why was it there?
And most importantly-- Is it likely to render my shirt unwearable?
Sounds like a hairball to me. Every so often one of mine vomits up little clearish pools with bits of food and typically I can find bits of hair in it. Sometimes it’s just pools with food and nothing else. But cats and vomit go together like, well, it’s just something to expect.
Well, it could have been a hairball, however, you asked if your shirt will be wearable or not so I am wondering if the “deposit” smelled foul. Hairballs generally do not have much of an odor. If this biological emmission was a revolting, nostril gouging stench, it may very well could have been from the kittie’s anal glands. My gf had our cat release her glands right on the gf’s leg. Gag. As far as the shirt, wash it with your regular detergent on a normal cycle but also throw in 1/2 to 1 cup of white vinegar in the load. That will take care of it.
There were only two, fingernail-sized bits of orange-coloured crud in a pool of clear, sticky liquid that was pretty large, and it did smell offensive.
Next time the missus ‘volunteers’ us to take care of someone’s animals, she’s getting a stern talking-to 
Yup, it’s probably a hairball. Easily washes out of clothing so you’re good there.
Tell the kitties parents to buy “Hairball remedy” It’s a meat flavored gel that you give them one inch out of a tube (like toothpaste on your toothbrush.) It helps them pass the hair in they get in their stomachs rather than horking them up.
And hey, make the wife go feed the cats if she’s the one that volunteered. 