There was a compilation of short stories in a book that I read in school in the '80s, but even then it seemed well worn, so I'm guessing that it might have been published in the '60s or '70s. It might have been labelled as horror stories, or scary stories, etc.
One story that I remember very well starts with a blind man sitting outside. He hears a strange person's gait as they walk by, it goes "shuffle, shuffle, click, click". He doesn't think much about it, but then encounters a man later on in an apartment who tells him that he has been on the run from a spirit or monster of some sort, ever since he helped to uncover a tomb in Egypt. He talks about how he dodged it here, evaded it there, etcetera and now he always makes sure that he has two escape routes wherever he stays... When he finally gets 'round to telling the man (maybe he was a locksmith or watchmaker?) about the sound that gives the creature away... the shuffle, shuffle, click, click, the blind man is astounded to tell him that he heard that sound earlier in the day. There is then talk about recent rain that might confuse or clarify the scent, and then they hear it in the hallway outside. The man runs to his escape route only to find that it is blocked and ends up jumping out the window. The blind man stumbles over his dead body later on the pavement and even though he is dead, he can hear the man running and the creature still shuffling and clicking after him... So he does not escape the creature, even after death.
Another story in the book involves a stuffed dog in a neighbour's house that is creepy and sometimes feels warm to the touch... I think that it harms a child that is visiting it at the end - or that is what is implied.