Using needle nose pliers to pull out a busted and stuck ramrod is NOT the way to go - the chances for buggering the muzzle crown are extremely high.
I'd doubt the rod busted clean at 90* and instead sheared off as the wood grain runs which leaves a slope for drilling in a hole to screw something in that'll allow the rod to be extracted.
IF the breech plug is of the patent ilk - which it will be for any offshore muzzy such as CVA, T/C, Lyman, DGW, Cabelas, Traditions, Investarms, etc - the stuck ball/busted rod fix is relatively easy.
The OP didn't say whether the ignition is cap or flint. Flint is easiest - unscrew the touch hole liner and load the patent flue full with powder (it will accept at least 20 grains or more), return the liner and blast whatever is stuck in the bbl out. Do the same with cap guns, remove the nipple and work powder into the flue.
The concept of dry balling or busting a rod down the tube is not will it ever happen, but when will it happen.
And yet again, the ability to remove any and all trad sidelock muzzy breech plugs has boo-boo proof benefits. Specialized tooling is not required, just makes it easier. Pulling and lubing the plug on a new gun and lubing it is a smart thing to do. Fired guns can be Difficult since the BP residue will have migrated into the dry plug threads. Some guns - notably Traditions - have plugs that are nearly welded in and near impossible to remove, even with a new and unfired gun.