Used to indicate an absence of any limit or end, expressing 'if one starts to …, there will be no end to it'.
Long explanation:
The grammar pattern ~ばきりがない is used when expressing that if a certain action is started, it won’t end or there is no limit. It conveys a sense of ‘if one starts to …, there will be no end to it’. Generally, it’s used when talking about negative things or infinite possibilities.