Dynamics of Short Selling on the Broker’s Side

Occasionally, I sell short a rather obscure class of stocks that might either not be available for shorting, or the amount that can be shorted is limited. It all depends on the ability of the broker to locate the stocks to borrow.

I am curious about the following scenario.

Let's say I want to short a stock ABC. The broker has reserves of stock ABC, which is basically the amount of ABC stock that all other clients hold on their accounts. Let's say it is 1000 units, and based on this number, the broker decides it can allocate 100 units for short sale.

What happens if I short 100 units, and then a massive sellout of ABC follows. The reserves that the broker has decrease rapidly, e.g from 1000 to 500, 300, 200, etc.

Can the broker force me out by closing my position? Or will it assume the risk of essentially being on the other side of the trade?

Thanks