Time-out value, when node is set to Forced Offline.

Well the time-out value is independent of different states like offline, forced-offline etc. Meaning it doesn't change.

The time-out value is defined in the profile which is mapped to the VS.

Default timeout values

Lets you have a connection established, which is an existing connection on the bigip table. As long as that session is not closed by Connection: Close in the header, its still an existing connection & not a new connection. On packet level your tcp port remains same throughout that connection.

Also if you start seeing in terms of redirection, the TCP port used by the client changes too. This would mean its a new TCP connection. Its no more an existing connection.

Based on the new connection or existing connection, the traffic will be sent to the available pool member, as in force-offline member will no longer receive traffic for new connections.