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when a node abnormal exited, that node still can be seen on the master ?

yes.

rosnode cleanup is a way to try and rectify such a situation, but it's not entirely without faults. See the linked discussion in #q9521.

How can I check the active status of that node?

I would say the same way rosnode cleanup does it: rosnode_cleanup(). It essentially "pings" (xmlrpc) all nodes it knows about and any node that did not respond are considered dead, and deregistered.