Two-dimensional calculations of the evolution of remnants generated by the strong mechanical energy deposited by stellar clusters in dwarf galaxies (M similar to 10(9)-10(10) M(.)) are presented. The evolution is followed for times longer than both the blowout time and the presumed span of energy injection generated by a coeval massive stellar cluster. The remnants are shown to end up wrapping around the central region of the host galaxy, while growing to kiloparsec-scale dimensions. Properties of the remnants such as luminosity, size, swept-up mass and expansion speed are given as functions of time for all calculated cases. The final fate of the swept-up galactic gas and of the matter processed by the central starburst is shown to be highly dependent on the properties of the low-density galactic halo. Superbubbles powered by star clusters, with properties similar to those inferred from the observations, slow down in the presence of an extended halo to expansion speeds smaller than the host galaxy escape velocity. Values of the critical luminosity required for the superbubbles to reach the edge of the galaxies with a speed comparable to the escape speed are derived analytically and numerically. The critical luminosities are larger than those in the detected sources, and thus the superbubbles in amorphous dwarf galaxies must have already undergone blowout and are presently evolving into an extended low-density halo. This will inhibit the loss of the swept-up and processed matter from the galaxy.