My friend has recruited me to find the title of a short story or book he read back in the mid-80s.
An alien was chasing a guy and he never ran but he never stopped, either. The guy was getting tired of staying one step ahead. The alien had wheels (? maybe?) and a syringe in one of his arms. Along the way he fought a bear and the bear put up a good fight but lost.
Alibris. Other than that, I suggest you consult your local librarian, and see if s/he can rustle up a copy of one of the F/SF anthologies that included it.