Cat on a Cold Tin Roof — Mike Resnick

Hard-luck gumshoe Eli Paxton is hired to find a missing cat--a very important cat, it turns out, because its collar is studded with diamonds worth a small fortune. What starts as a routine search of animal shelters soon becomes a perilous journey through a murky underworld. The woman who hired Paxton is the wealthy widow of a recently murdered financial adviser with an alias and mobster ties.

Paxton finds the cat, but not the collar. Eventually, he's forced to unravel an intricate plot involving a Bolivian drug cartel. On top of all this, the temperamental widow is more likely to throw things at Paxton than pay him for his services. 

As he turns up one clue after another, leading him ever deeper into a treacherous maze, Paxton hopes, first, to survive, and then to make enough money to afford a new transmission for his broken-down car.