That is not always the case, certainly not in modern times. If you have a full service broker and there appears to be sufficient time to contact you, they may do so and give you a chance to pick what to close out.

However, very few people use full service brokers. Everything is now automated. The best you can hope for is that the broker provides a mechanism prior to the need to close any position to signify which should be the last one hit to pay the margin loan. As a specific example, Interactive allows their clients to pre-select one holding as the absolute last one to close.

(edit spelling)