In the year 2130 all of the Bitcoins will have been mined and the only reward at this point is transaction fees,if most people are using Bitcoin just as a store of wealth, then there are very few transactions,
OP has a valid hypothetical question but my answer is a straightforward No!
Bitcoin will not become inactive especially when all of it has been mined and thus will result to a more wider distribution of it.I think there are two possible scenarios concerning mining that will come into play when all Bitcoin has been mined:
1. Bitcoin's price has achieved its ATH by then that mining it (even if the rewards comes from transaction fees) is still attractive or could be more profitable than the current mining situation right now.
2. Bitcoin's miners have ceased to do mining but will eventually be replaced by stakeholders, enthusiasts and supporters who want to "keep the network alive" and eventually protect the value of their Bitcoin holdings. So, mining will still continue no matter what. Imho.