Does anyone know if its possible to make a gift of property to a relative and for the property to no longer be part of an inheritance upon death?
In general, a person's property is theirs to do with as they wish; so it is in general entirely possible for a person to give their property to anybody and for that property to therefore not be part of their estate. However, the transfer would need to be performed legally and any tax matters would need to be taken care of.
If a person made a gift of property in Poland and later passed away, could other relatives claim inheritance, or would it rightfully belong to the person to whom it was given?
That would depend on whether the transfer was made in the correct legal form, which itself will vary depending on what kind of property you are talking about.
Reading between the lines in your post, you may well either want to know if you can claim property which used to belong to a now deceased relative or if it possible for a living relative to in effect not leave you or some other person something in their estate; whichever, you really do need to speak to a lawyer.