Yes it does. I find that it takes 3 or 4 coats of oil for the dye to stop rubbing off.
The way i do things, was taught to me by englishman_ca (more like explained via emails)
I apply multiple coats of Fiebings dye, until the wood doesn't absorb it anymore and the color is pretty much opaque.
The first few coats go on fast because they dry quickly.
I then let the whole stock dry for several days. A week if i can resist the temptation.
Next comes the linseed oil.
I lightly heat the oil and slap it on the stock with a rag, wait 30 min. and wipe any and all excess with kitchen paper towels.
This is were it is messy as any dye that has not penetrated in the wood pores, rubs off too.
No oil should be left on top of the wood, what ever hasn't penetrated has to be wiped off.
Let dry and repeat the same process 24hrs later.
I usually do this 3, 4 even 5 times.
At that point any surface dye should be gone and i will also have build a base layer of oil on the stock.
I then start to oil again but this time, before wiping the excess i use a very fine steel wool and rub it all over.
The force i use depends how much i was to ''sand'' or ''rub off'' even more dye.
This is were the matching of different color of wood happens... rub hard on dark wood, rub light on light wood.
Again i do this as many times i feel i need. Maybe 2 - 3 times, it depends on each projects.
During that time, sometime i will also use straight black to had stain spots here and there. The very dark, almost black spots often cause by cosmolineand rust we see on almost all Lee Enfields.
Those are great to help to hide repairs and splice lines. Instead of a very straight dark line you have a wavy with gradual strength and hardness spot that helps fool the eye.
It's not always desirable or possible but effective when it is.
Once i am satisfied with the color, i apply oil my usual way... soak the stock with a rag, wait 30 min and wipe the excess.
I find that a good staining job will almost always require multiple coats of different kind of dyes and/or stains.
This is what gives it character and depth.
The wood should not be sanded too smoothly to start with and i even wet the wood to raise the grain even more before applying the initial stain.
The steel wool will take care of that and i also finish (before the final coat of oil) by what englishman called ''boning''.
Using a bone or anything smooth (i use a round metal object and a leather creaser tool) to rub the entire surface to give it a rubbed almost polished look that only old rifles that have been handled for many decades, have.