Can You Still Get Unemployment If You Owe Them Money?

Depends on "them"
If you owe your former employer(s) money, that has no bearing on current lack of work entitlements. If you owe UC funds back, it is probably because they determined you received funds you weren't entitled to. There is probably a block on your account preventing the filing for benefits until the balance is cleared up (plus they'll add interest to the balance). Afterwards (if they still determine you haven't lost your eligibility) you can file for those weeks, but you may need to schedule an interview, or appeal for a hearing to get your status reinstated.

Lots of red tape and lousy attitudes: They can stop your disbursements within 24 hours of a determination, but could take 30-45 days to straighten out the mess, then another 21 days before they release the appropriate funds. Good Luck.