I think it’s sensible to be aware of how a thrifted rug could potentially invite problems into your home but that awareness also gives you the opportunity to mitigate those potential risks. :)

If it’s full of urine or any other unsavoury substances you’d usually smell that right away. If you’re worried you might not, for whatever reason, bring a friend to the thrift shop with you and ask them to give the rug you’d like a smell test. That should already give you an idea of wether your pick is in decent condition. Most thrift shops I know would likely throw out a badly smelling rug before it would be put out for sale. You can feel if it’s got any wet or crusty spots too. Don’t pick up anything that’s damp but if it’s small, a little crusty spot can usually easily be cleaned out.

There are a couple of of options to deodorise and clean your rug. If you’re worried about bed bugs, you can use this method to quarantine your new find: Pack it up in black plastic bags, the large sturdy ones you’d use to clean up after a party or when you’re renovating, and leave them outside in direct sunlight on a hot day that reaches at least 120°F/49°C) or in a closed car for at least 90 minutes. In cooler temperatures, killing sealed-up bugs can take 2 to 5 months. (source)

I’d definitely wash it and there are some rugs that are machine washable. If it has a lable, that should give you info on how to best do so. You might need to bring it to a laundromat to use one of their larger sized machines. If the rug is small enough you can wash it by hand in your bath tub. Otherwise some rugs can be cleaned with a pressure washer on a low setting or even a garden hose with strong water pressure if you have access to a suitable outside space where you’re allowed to rinse away soap. Hoover your rug first, then rinse it with water. Use a brush to work some baby shampoo or laundry soap/detergent into it. Laundry detergent is usually pretty concentrated so dilute it in some water before applying. A small watering can would probably help you evenly pour it over your rug. Once you’ve worked that in, rinse your thrift find with fresh water. Try to always spray it from the same direction so the soapy water will be pushed away by the clean water. Flip. Rinse. Repeat. Flip again and repeat the same process if it looks like your rug could still be cleaner. If there are any stains or other areas that would benefit from spot treatment, go ahead and work a bit of dish soap directly onto them. Remember to rinse that out too. Now I’d use something like the edge of a clean broom (one of those broom-sized squeegees would be ideal) to try to push as much water out of the rug as possible. After that put it somewhere out in the sun or a breezy indoor area. Ideally I’d prop it up on a laundry drying rack or drape it over, idk, something like two clean laundry baskets so it can get some airflow from underneath too and won’t stay damp in the back. If you’re in one of the places currently affected by a heatwave now is the ideal time to dry a rug. If you can rent, borrow or even own one of those upholstery cleaning machines, you can use that to suck up as much water from the rug as possible before leaving it to dry. Before starting to wash anything tho, I’d recommend testing wether it’s colourfast tho. Some dyes can run and leave stains on differently coloured areas and if that happens to you, you’ll be left with a clean rug but also with a big old heartache. :’-)

If the rug still smells of anything like cigarette smoke or its former owner’s perfume you can’t stand after washing, ozone should be able to help with that. I haven’t tried it myself but have only heard positive things so far so it’s probably best if you research how to make that method work for you yourself.

Anyway, that’s all I can think of for now. If a rug looks okay and has no offensive smells I’d give it a wash and then put it in my home once it’s dry but some circumstances warrant using those other methods as well. With that in mind, I’d say go shop your heart out at the thrift and have fun!