I didn't know this before looking it up yesterday but, unlike most bike manufacturers, Trek does indeed seem to offer limited warranty coverage for a second or third owner:
https://www.trekbikes.com/us/en_US/warranty_policy/
It's three years from the date of purchase and you must have the purchase receipt/invoice to prove date of purchase. That three year warranty period, according to their website, covers the frame and fork only.
This is more than most manufacturers offer, but it's still significantly less value than your coverage if bought new.