[venuzr]

Yes. The parent's visa can be transferred, for up to a max of 6 years in length. However, the employer needs to be willing to transfer the visa. Lots of employers are willing to transfer the H1B during a good economy but rare to find an employer who would be willing to do so in a bad economy.

Also, if H1B worker wants long term stability and wants to stay in the US beyond the 6 yr period, then the employer needs to apply for Permanent Residency (Green Card). The H1B worker needs to employed for that employer for the entire duration of that GC process. The icing on the cake is that the H1B worker needs to find new employment within a month of being terminated or leave the US. Again, possible in a good economy but near impossible in a bad one.

All in all, this creates the perfect hostage scenario with H1B workers pursuing stability till they get their green card.