In 1941/1942 Nazis captured Polish and Ukrainian citizens for their OSTARBEITER (Forced Labor) Program.
Germans kept exact records of anyone that set foot in their territory during WW2. Contact the Bad Arolsen Archives. After the opening of the archives appx 4/5 yrs ago, there are still miles of shelves loaded w/DP (Displaced People) records, that are being digitized. Bad Arolsen will provide you w/records of Immigrant Family's exact experience in Germany, including personal details like place of EXACT origin and what Family Members were doing 6 mos prior to their German exp.
Inquiry by immediate family is available for free. All you need to provide is the full name and any other spelling variants or name variants and the exact birth date or as exact as you have it. Your inquiry can be performed by e-mail. Turn around can take as little as three days or nowadays as much as six months.
Upon accessing site click INQUIRIES BY FAMILY MEMEBERS. Follow instructions.http://www.its-arolsen.org/en/homepage/index.html
Another valuable link for DP descendants:
Displaced Persons' (DP) Camps Table of Contentshttp://www.dpcamps.org/
Once you have the exact place of origin, it will not be too difficult to ascertain whether there is still surviving family living in Ukraine. I will be more than happy to help you do that.