It didn't. The destruction was an event of so little importance that there are few sources mentioning it, truth be told. This topic appears quite often, so you might be interested in the following responses:

This reply reply [account deleted, so I can't give due credit] presenting the concise timeline of the Library's history.

This thread where various details of the Library's inner working is discussed.

This reply by /u/XenophonTheAthenian focusing on the the (lack of) importance of the loss of Library and the texts stored there.

My previous reply detailing the events that led to the actual destruction of the Library's buildings and some misconceptions related to the event.