Jasper is secretly Very Strong from a lifetime of lifting bales of hay. He has also probably had to slaughter or at least witness the slaughtering of various farm animals, so he is more acquainted with death than most of the Lodgers. (Actually I'm not sure about that--the Lodgers come from pretty diverse walks of life--but he's definitely more familiar with death than Jekyll.) If he were to ever lose control in wolf form and be shot dead by the police, he would have a pretty good idea of what that would look like, and he's accepted that this might happen to him some day.
And yet he cannot bring himself to go down and talk with the other Lodgers! He's so scared of it! Even though they've generally been nice to him! Jasper is more okay with dying in the street like a rabid animal than he is with a roomful of his peers being silently disappointed in him.