By now, you have read enough answers here to know that SOME conicals will move in SOME guns!
If you check with suppliers, like Track of the Wolf, Cains, etc.( see the links section at the top of the index page to this forum) they sell Over Shot cards in most calibers and gauges. You can buy these for your particular gun.They will hold the bullet on the powder, yet not affect the accuracy of the bullet when the gun is fired.
The larger the caliber, the more likely that a bullet of any weight will move. It has to do with the degree of arc, and coefficient of friction of the bullet to the bore, but just leave it at a general understanding that the heavier slugs in larger calibers can move forward easier.
If you use some kind of cloth patch already, these can also be used as an Over bullet wad, to hold the bullet in place. But, you usually have to use a couple, and they have to be greased( so the fabric doesn't dry, as it would if they were damp with any water or alcohol based solution).( IMHO, the OS cards are less hassle.)
In the old days chunks of hornet's nesting were used to hold both bullets, and shot loads in smoothbore barrels, which are more likely to allow movement of any bullet, than a rifled barrel will. So, hornet's nest can also be used to hold your bullet in place.
If you err on the side of caution, by checking the postion of the ball after any movement of the gun, as described above, you are not going to have problems. If a bullet were to " fall out the muzzle", the worse thing that happens is that you have to dump any powder left in the barrel out, and then RELOAD the gun.
Some conicals are " stepped", they have a driving band at the front of the bullet that is larger than the bore(land to land) diameter of a rifle. When you load that kind of conical, the bottom of the bullet fits snuggly to the bore, but that last band requires a sharp "whack" of your hand on the short starter to get it seated in the rifling. The typical hollow base on these conicals will open up the back of the bullet when fired to provide a gas seal, of sorts, while that drive band keeps the bullet centered in the barrel. It also provides enough friction that the bullet is not likely to move during movement of the gun to, and in, the field.
So, choose your conicals wisely. Some really ARE BETTER than others.