WELCOME to YT and bless your heart for adopting Jaxson
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I wouldn't be surprised if some of his personality is still repressed right now. Who knows how he became homeless or what transpired. Also, shelters are often extremely stressful for dogs - the noise, the fear, the smells, the anxiety from being caged up. Some former shelter dogs take a while to come out of their shell again. Do you know how long he was in the shelter?
Hang in there with the poopy thing - I'm sure it'll get better over time; I agree with you that it could be some kind of anxiety. He will get there with your guidance.
We have some rescue folks on this board, and they may be able to offer some insight too.