what are the chances of my wife returning to US on immigrant Visa she overstayed but has completed the 10 year bar
She has a good chance of success. However, as the previous answer suggested, the immigrant visa packet needs to be well documented to prove that she indeed stayed in her home country for 10 years.
Best of luck.
Verdin Law Firm
If she was subject to the ten-year bar but has complied by remaining overseas for ten years, with no entries or attempted entires to the U.S., this shouldn't hinder a new application to return to the U.S. assuming no other grounds for exclusion.,
One issue may be documenting when she left and her presence overseas for the ten years - passport stamps, leases, job records, etc. may be critical here.
Another issue - if she has remained there the last ten years while you have been here - may be documenting that the marriage is bona fide (real).
Speak with an attorney to determine what other issue may exist specific to your case, and how best to deal with them.