That really cannot be repaired at all. You would basically need to dismantle the door and remake the stile which will require considerable machinery.

If it's not rotted at a stress point, you could do a cosmetic repair that would probably have a 'rustic' appearance.
After whitling away the deteriorated wood, you can then apply an application of a wood restoration putty which can be sanded smooth to the desired shape and painted after it cures.
There are several on the market; J-B Weld, Red Devil, WoodEpox to name a few.
Bondo automobile dent filler can also be used.

randy...thank you. What you stated is exactly what the antique shop told me....since it is being used inside as a pantry door, structurally it is sound enough to have a nice look.
Thank you!
Pam

What about those products that are supposed to soak into rotting wood and harden them? Not that it would change how this door looks, but wouldn't it stabelize this a bit?

Sure it can be repaired! But it would have to be either painted over, or do some sort of faux wood color in that corner over the wood fill (if its at bottom or top, who's going to notice.) you can use the epoxy wood fill to fill in gaps and even build out the corner (sanding it flat on all sides.) If you are an artist and can do detailed work, you wont be able to tell its wood fill and its not going to look "rustic" - itll look great! If you are Not an artist - then it might not look so good!

Dont use Minwax or any big box wood fills or hardeners - it is not durable and really is an inferior product compared to the Abatron. I used Abatron on a number of exterior repairs - sills, even rebuilt a window sash and all have lasted quite well thru rain, sleet, snow, 100 degree days.. No, I dont work for them!!! Used in historic renovations everywhere, interior exterior. More expensive than big box products but worth it in terms of durability and still more cost effective than buying new. The really soft, crumbling wood has to be removed but if its just soft and spongy but still intact - that can be hardened quite nicely.

It can be repaired. You can start with removing old weatherboard from door. The wood must be completely dry before tackling this repair. Apply wood treatment solution to the affected timber. Leave for at least 24 hours and brush on a generous application of wood hardener. Apply further coats if required. Allow to dry overnight and fill any cavities with wood filler.