Is it common for prestigious universities to contact you after you dropped out to see whether you wish to enroll again? Many months ago, I had to drop out from a prestigious university.

Lately, the university contacted me and asked me if I were considering enrolling once again, and said that if yes, I should do so before a certain deadline.

Is it common for universities to contact drop outs?
The answer may depend on why you had to drop out, but many universities simply consider you to still be their student even if your studentship is disrupted by events beyond your control, and will assume you are likely to wish to continue your education there.  

You do not say why you had to drop out, but common reasons for somebody to withdraw or fail include: mental health issues, financial crisis, physical illness, death or serious illness of a close family member, visa problems, etc.  None of these indicate anything negative about your potential as a student even if they caused you to fail all of your classes.  I have known people who dropped out for a wide variety of such reasons, many of whom then returned to finish at the same prestigious institution after their life circumstances had improved.

Many universities thus make it easy for a student who left for such circumstances to return and complete their studies, and that is likely what is going on with your university as well.