Depends on your responsibilities. Do you have people to support? Multiple sources of income? How reliable is your health? You parents health? Your car?
What you're basically asking is the old question of Emergency Fund or Debt? The answer is usually enough of an emergency fund that an emergency doesn't make you dip into more debt.
I would say the answer is that you should have enough of an emergency fund that an emergency doesn't make you dip into
worse debt, not necessarily "more" debt.
For example, if you have $10,000 in student loan debt at 5% and an emergency would require you to put the expense on a credit card at 20%, then yeah, you should have an emergency fund to cover that.
On the other hand, if you have $10,000 in credit card debt at 20%, then you should pay it down and skip the emergency fund because even if you had an emergency and the balance went back up again, you still saved money on interest compared to carrying the high balance while holding cash.
On the third hand, if you were at the 5% student loan scenario but had a 6% HELOC you could tap in an emergency instead of a 20% credit card, maybe you'd be better off neither holding cash nor paying down the debt, but shoveling extra cash into investments instead.