Something is not right here.
The Product Backlog is an ordered list of everything that is known to be needed in the product. - The official Scrum Guide
It is almost inconceivable that everything that is needed only amounts to half a Sprint's worth of effort!
Perhaps you meant that of all the many items comprising the Product Backlog, only half a Sprint's worth meet the team's definition of ready? In this case, the Product Owner is not doing their job properly and the Development Team and Scrum Master are failing to hold the PO accountable for their failing here.
There is a story in Scrum, possibly apocryphal, of a company where, if the PO had not done their job properly and there were not enough work ready to play, the development team were allowed to go to the beach, and made sure they nosily passed the CEO's office on the way. Certainly a the rule of a Scrum Team I worked on was that if there was no ready work then we were to sit with our feet up on our desks. Although this sounds silly, the idea in Scrum is to make impediments visible and sitting around with feet up on desks sends out a very clear message, as does stampeding outside the CEO's office, I imagine. Of course, developers should be aware of their own responsibility as regards preparing Product Backlog items.
A practical approach might be to take all the ready work into the Sprint Backlog, with the aim to finish it all well before then end of the Sprint, and plan to use the remaining time in assisting the PO in getting more items ready for the next few Sprints. There should ideally be three or four Sprint's worth of PBIs that are ready at all times (and this should be achievable after a few iterations where Sprints are purposely finished early). Any more than this would probably amount to waste.