As per the immigration law, a person in out of status immediately the position is terminated.

There isn't any so called 'grace period' after that. USCIS has proposed 60 days time as grace

period but this hasn't become law yet. With the same fact mentioned, theoretically person should

immediately leave the US soil.

But leaving county immediately is not practical, lawyers suggest 10 business days is reasonable

time to wrap-up the personal affiars in the US before leaving the country.

As per the question of finding new job, I am not certain on this. As your current H1B status is

terminated, I don't think you can apply for H1B transfer. Your new sponsor may file petition for

new H1B, but as per my understanding, that won't be possible for this year. I think, this needs to

go as a new H1B application pertaining to H1B cap.

 

This response is simply an information as per my knowledge, better consult a lawyer.