Can a manger take an employee sick time and give it another employee?

So lately I haven’t seen my Boss in three weeks, for some unknown reason. And the director (who is my boss’s boss) send a massive email about a position opening for my manager job, that my team has a new manager. So, to make a long story short, many rumors were going around saying that the old boss was stealing other employees' PTO/sick time and giving it to other employees. I don’t think that’s possible, so I’m asking this question.