Sorry to hear about that experience.
If you were asked to leave because of ethical or legal reasons, then you will not be able to join back the firm.
If you were asked to leave because of performance issues, I highly doubt you will be able to apply again.
- In my 8 years of consulting I have not seen this scenario before
- This is because most of the time people who get counselled out realize that consulting is not their cup of tea, and the firm realizes that you are not cut out for the job
However, what I have seen, and not as uncommonly as you'd think, is people who get counselled out shifting from one MBB to another MBB, or from MBB to T2. What you could do now is to
- Check with the actual recruiter - only they can give you the real, trustable answer
- If you are still interesting in consulting, focus on applications to other firms
Lastly, keep in mind that there are many, many, many other interesting and fulfilling jobs out there other than consulting.
All the best!