All roses can occasionally send up new shoots from the base, but with own-root roses, these shoots will always be the same variety as the parent plant. These shoots are a sign of the rose's health and vigor, as it's rejuvenating itself with fresh canes.
In contrast, grafted roses can send up suckers from the rootstock, which is a different variety from the grafted portion of the plant. Keeping an eye on suckers from grafted roses is important to maintain the desired variety.