There’s a pretty silly plot point about “blood thinners” in an old flash-based detective series, Nick Bounty.

Nick works out that a dame has been poisoning the town, and goes to confront her. She shoots him. He has no vest, but somehow he’s not bleeding. Nick admits that he realized he’s been taking the poison unknowingly during his investigation, and so his pulse had already been grinding to a standstill, hence no bleeding. He figured his best chance was to delay the culprit until reinforcements came.

Then, paramedics come and easily revive him thanks to no real blood loss.