We suggest the incorporation of remedial actions for profit-oriented disassembly lines with stochastic task times. When task times are stochastic, there is a probability that some of the tasks are not completed within the predefined cycle time. For task incompletions in disassembly lines, pure remedial actions of stopping the line and offline disassembly are proposed along with the hybrid line which is a combination of the two pure remedial actions. The remedial actions have a significant effect on the expected cycle time as well as the expected profit due to line stoppages and offline disassembly, which together make up the incompletion costs. Stopping the line allows the line to be stopped until all incomplete tasks are completed, while in offline disassembly, incomplete tasks are completed in an offline disassembly area after the core leaves the line. The approaches used in assembly lines for quantifying the associated costs with stopping the line and offline repair for a given line balance are modified and used. Hybrid lines can implement both pure remedial actions for two different task classes: The line is stopped for Finish (F-) tasks and offline disassembly is executed for Pass (P-) tasks. For hybrid lines, we formulate the problem for given line balance so as to maximize the expected profit as a Mixed Integer Programming model. A full enumeration scheme is proposed to derive the hybrid line solution. As partial disassembly is allowed, for offline disassembly and hybrid line, we also formulate and solve the task selection problem so as to determine which incomplete P-tasks to execute during offline disassembly. Our computational study aims to show the significance of incompletion costs, analyze the effect of the base cycle time and demonstrate that hybrid lines are capable of improving the expected profit as well as expected cycle time compared to the pure remedial actions. Stopping the line and hybrid line on average yield 26% higher expected profits compared to offline disassembly.