Legal Question in Criminal Law in Texas

No. The property was abandoned.

Suppose the purse was reported stolen. Suppose it actually was stolen and the thief abandoned it on the trash can.

The problem you face is that only true owners can abandon property. Second if you are found with the purse, and charged with theft, how do you prove that you did not steal it?

My advice is to look in the purse for Identifications and try to contact the owner. Send letters and make copies. If there are no ID's in the purse, call the police to see if there have been any reports of stolen purses.in the area. If no one claims the purse after a resonalbe period, you can keep it and its contents with the knowledge that if you are accused of theft, you will have proof that of your efforts to find the true owner.