Yes, that's the big question here. If it's a margin trade, the broker is also a lender and has some discretion. If it's a cash trade, the broker has no risk and should not interfere. Does anyone know? This matters.

100% they're on margin. Otherwise the broker would have no right to make trades on their behalf.

In contrast, once you're on margin you give them the right to liquidate any part of your portfolio, at any time, to cover your margin balance.

What they can't do is liquidate beyond the margin balance. Once they've covered the balance they would have to stop closing out your positions.