If they don't pick it up or keep returning it to you, then see if you can find the number for the sender and call them. If still nothing comes of it, then you tried and it's yours to keep.

It's never yours to keep really. In most countries opening or keeping it would be a crime, but skipping that the company has 3 years to realise their mistake and bill OP. It is however not your responsibility to drive it back, just have then pick it up, or if you're feeling generous drive it back but have them pay you for gas.

OP here. 1) I looked for a company phone number but could not find one (all I discovered was it was a medical supplies company). 2) I called UPS several times. I called immediately both times. First time it happened, I asked them to come pick it up. They said they would need to charge me for said pickup (even though it wasn't my package). They said if I dropped it off, there would be no charge, so I dropped it off and I told them to return to sender. That's when it came back the next day. I called to complain again and all the guy had to say was "yeah someone didn't do their job. This actually happens a lot, not the first time, won't be the last time". I ended up dropping it off again and chewed them out. Funny thing was the SECOND TIME it was delivered, I was home. I recognized the dang box right away and tried to catch the delivery man but he was already racing off to the next delivery. Wasn't really a huge deal, more less funny...try to do the right thing and the stupid box comes right back like some sort of curse...but I haven't gotten it back again and hopefully the old lady gets her medical supplies soon :)

Very few packages require signatures, as much as people ship stuff nowadays it'd make it extremely difficult to require it on every package