The people who companies want to keep are those who step up when times are tough. They're team players, they're always willing to take on another project, and they pick up some of the slack when others are laid off.
Perhaps more importantly, these people also make these qualities visible to the top dogs. I'm not saying you should email your boss an update of what you're doing every day, but it doesn't hurt to volunteer to put in a few extra hours if needed or take the lead on a big project.
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