Suckering trees, shrubs and climbers and raspberries can be propagated from suckers (shoots arising from the roots). Providing they have produced their own root system, it’s a simple matter of carefully digging them up and either potting them up or replanting them where you want them to grow.
Suckers produce a new plant quickly and easily with little effort as they already have their own root system. The drawback is that you have to wait for them to appear naturally – although you can sometimes encourage them to form by wounding the main root. This is not necessarily a good idea, since wounding may not produce suckers, may cause disease to enter the root and once done can encourage a thicket of shoots to be produced.
Grafted plants cannot be propagated from suckers. The suckers arise from the grafted rootstock, and only this will be propagated – not the named plant/variety grafted onto it.