Hello Nami
If the L1 holder leaves for more than a vacation (ie: goes off the payroll) then L2 is immediately out-of-status. The key is the purpose of your departure. If you are leaving for a temporary period only, and remain employed with the company, L2 should be able to remain and work in the United States. You are a derivative of your spouse L-1 Visa status.
So to answer your question Yes you can stay back in US without him as long as your spouse is on a US payroll.