This is difficult immigration question what if H-1B holder is in his/her sixth year (last year) and a PERM case is not filed on his/her behalf? Can Immigrant live in US for another few years?

Yes you can says this news. Basically get away from H1-B status and remain in other status say H1-B or a student visa like F1. File PERM and then wait for a year and get back to H1-B visa status where an eligibility extension is possible.

But make sure the changing status to other visa types is not a time taking process otherwise one would go out of status after six years.

The site lists all other possible visa categories that a person can use to move away from H1-B :

B-1 or B-2 (temporary visitors), E-1 and E-2 (owners or workers with trade or investor visas), F-1 (students), H-3 (trainees), J-1 (international exchange visitors), L visas and more. Of course, not all of these categories will be available to all aliens, and even when available, they may not necessarily authorize employment.

Have you been in this situation and Are ther any other alternatives than moving away from H1-B status? Please share with us