grep '/$'
slash is not special character for grep and $ means match expression at the end of a line.
You can even grep the last column with only backlash at last column (but not the only column in the line)
I assumed tha the last column of a line is a string with more than one white space in front the string and no more character after the string. This assumption does not fulfill the requirement if there has only one column in that line because it does not need space in front of it to show it is last column if there has only one column.
By enable perl regular expressions (-P),
grep -P '\s+/$'
\s means matches any whitespace character (space, tab, newline)
plus sign means match 1 or more times for preceding element
$ means end of string
OR refer to Character Classes and Bracket Expressions
grep '[[:space:]]\+/$'
OR
grep '[[:blank:]]\+/$'
‘[:blank:]’ Blank characters: space and tab.
‘[:space:]’ Space characters: in the ‘C’ locale, this is tab, newline,
vertical tab, form feed, carriage return, and space. It is a synonym for '\s'.
Refer to @fedorqui, the backslash after ]] is used to distinguish with
the literal +. Thanks for the explanations.
Sorry if wrong for perl answer because I never use or learn Perl expression but really hope can help you find the last column slash so may be you can read these for more information for searching backspace with slash at end of line
grep with regexp: whitespace doesn't match unless I add an assertion
Regular expressions in Perl