Should I force myself to finish meditating if I keep falling asleep?

If you keep falling asleep during meditation, rest first and sit again when more alert. You need not force yourself to mix sleeping with meditation. I have also fallen asleep while sitting. Even if someone says they slept enough, I cannot determine the cause for them over the internet.

If sitting brings distraction, try counting breaths and placing attention on breathing. Count one inhalation and exhalation as one, go from one to ten, then count backwards. Alternatively, count one on inhalation and two on exhalation. This supports concentration; everyone need not use precisely the same counting method.

If you have rested and tried counting but still keep sleeping, temporarily read scriptures or recite them instead. My suggestion to that listener was to look at the words and recite aloud, giving attention something to do. It was not a claim that all silent recitation is ineffective. Care for your condition first, then consider how to arrange practice.

Your schedule matters too. Because I stayed up late, someone once asked whether I slept only two or three hours daily. I explained that I rose late and worked in the afternoon, still getting six, seven, or eight hours. Bedtime alone does not establish whether someone has enough rest.