In some cases, yes. For example, MedPay will usually cover any medical bills not covered by the at-fault driver’s insurance. UM/UI policies come in two types, stacking and non-stacking. Stacking policies will give you additional coverage that “stacks” on top of the other driver’s coverage. So if they have $25,000 in bodily injury liability, and you have $25,000 in a stacked UM/UI policy, and your medical bills come to $50,000, you should be able to get them all covered.
However, if you have a minimum non-stacking policy, it will only guarantee that there is $25,000 in bodily injury liability available to you. If the other driver’s policy pays that, the non-stacking policy pays nothing. It’s important to read your policy carefully to understand what kind of coverage you have.