EDIT 2: just realised this doesn't actually resolve your problem, please ignore and see other answer! The code below will return results for a case when a user has inserted an apostrophe which shouldn't be there, such as "abandoned it's cargo".
I don't have FT installed locally and have not tested this - you can use the syntax of CONTAINS to test for both the original occurrence and one with the apostrophe stripped, i.e.:
SELECT *
FROM table
WHERE CONTAINS ('value' OR Replace('value', '''',''))
EDIT: You can search for phrases using double quotes, e.g.
SELECT *
FROM table
WHERE CONTAINS ("this phrase" OR Replace("this phrase", '''',''))
See MSDN documentation for CONTAINS. This actually indicates the punctuation is ignored anyway, but again I haven't tested; it may be worth just trying CONTAINS('value')
on its own.