What keeps bristles supple during storage is proper cleaning of the brush after use. If the brush bristles become stiff, it means that there was still finish in the bristles when you stored it.
Here's the proper brush cleaning process:
First, the best way to make a brush easier to clean is to dip the bristles into mineral spirits before you start to use the finish. This will prevent finish from getting up into the ferrule.
For cleaning, use a big 3# coffee can. I pour in some mineral spirits and work the brush in it until is is as clean as you can get it. Then twirl the brush handle between your hands to remove the cleaner. Then pour the cleaner into a smaller 1# coffee can. Now pour some more mineral spirits into the large can, work the brush, twirl it and pour the cleaner into a second small 1# coffee can. Cover both coffee cans. The solids will settle out and the next time just pour off the liquid from the first can you used into the large can for the first rinse, then pour off the liquid from the second can for the second rinse and so on. When the first rinse can gets too full of solids, pour off the remaining liquid into can #2 and add some kitty litter and discard the coffee can with the solids. Can #2 now becomes can #1 and you start a new can #2 with fresh mineral spirits. This way you never have to discard mineral spirits.
I final clean my brushes with water rinsable brush cleaner--which I save also--followed by liquid dishwashing detergent. Use warm water, not hot. Shake them as dry as possible and brush them back and forth on paper towels, then wrap in brown paper, fold it over t0 shape the chisel end of the bristles and hold with a rubber band.
You should never have to throw out mineral spirits and your brushes will be soft as new when you go to use them again.
If the bristles are stiff when you go to use the brush later, just put the brush into the brush cleaner for a few minutes and it will be soft as new. Shake out the brush cleaner and work the brush in a little mineral spirits to remove the brush cleaner before using the brush.