Epithelial tissue generally exhibits functional repair. Most epithelial tissues exhibit rapid mitosis and the original function is normally retained. Although the tissue itself has no blood vessels, vessels are a short distance away in the supporting connective tissue which is usually areolar. Epithelial tissue in the skin, in the linings of organs in the GI and respiratory tracts, in the liver, many glands, and in blood vessels can all replace and repair themselves, the limiting factor generally being the degree of damage and other nutritive and health factors.
Connective tissues with two notable exceptions have poor vascularization and therefore slow repair and replacement. And the repair of connective tissues (notwithstanding the two exceptions) is stromal repair, scar tissue which binds the organ but is not the same as the original tissue. The two exceptions are areolar, which is the route for blood supply in the skin and in many internal organs, and bone, which is richly supplied with blood vessels.