It depends...
Some states don't care if the trailer is over a certain age.
You may also get away with declaring it a "homemade trailer" as is done in Arizona a lot.
It also depends on what type of trailer it is. A cargo trailer can easily be licensed without a title. They get stolen all the time here.
It also really depends on who is selling it to whom, and if the seller is willing to create a bill of sale, and have it notarized.
You may want to ask the seller why there is no title, and if there is a purchase history they can relate, other wise maybe walk away.
You may also try asking the local MVD and give details, even the VIN if you can actually read it on the tongue. They may be able to trace it.
If the seller is willing to take it with you to the MVD for an inspection, that may help you get a title, maybe even a salvage title.
It Depends...