I'd say the exact opposite applies to layoffs. Most of the people who got surprised by them here were very popular with others. Relationships might matter more in peaceful times, though.
It looks like the main advantage of doing large scale layoffs is that it allows you to fire popular people who have contributed a lot and done nothing wrong, only committing the crime of being overpaid or being less valuable in the current market situation.
Someone who is the opposite - an asshole who gets shit done, has high odds of being fired-replaced during peace time, but may make the cut during a layoff.
Popular with others is a bit different than popular with your manager's managers, which is what the OP suggested. But one good way to get noticed up the management chain is a combination of high impact deliverables and self promotion so getting shit done is always a great recommendation.
It looks like the main advantage of doing large scale layoffs is that it allows you to fire popular people who have contributed a lot and done nothing wrong, only committing the crime of being overpaid or being less valuable in the current market situation.
Someone who is the opposite - an asshole who gets shit done, has high odds of being fired-replaced during peace time, but may make the cut during a layoff.