A suffix attached to the -masu stem of a verb meaning 'might well ...', 'it's not unlikely that ...', often implying a negative or risky outcome.
彼はうそをつきかねないので、信用できない。
He might tell a lie, so he can't be trusted.
そのまま放置すれば、重大な事故につながりかねない。
If left as is, it could lead to a serious accident.
無理を続けると体を壊しかねないから、少し休みなさい。
If you keep overdoing it, you could damage your health, so take a break.
渋滞がひどくて、会議に遅れかねないと心配している。
The traffic is so bad that she's worried she might be late for the meeting.