Obviously it won’t help you with your calibre of rifle but with the old classic rifles, Lee Enfields in .303 & 7.62 and possibly other service rifles from around the world, Burst Case extractor’s were produced, mainly used by the armourer.
When the case head had separated leaving the body of the case behind the burst case extractor (similar shape to a cartridge) was inserted into the action then pushed forward by the bolt entering within the case extending beyond the case mouth whereupon the collar of the extractor engages with the case mouth when the bolt is closed, open bolt extracting the burst case, it’s as simple as that.
Sorry my explanation is a little long winded.