Rescue procedures (RP), triggered either by the occurrence of the mission failure or by a certain undesired system state, are usually applied to survive a life-critical or safety-critical system mitigating or avoiding costly consequences. Existing works model either the mission failure-triggered RP or the system state-triggered RP, but not both. This paper makes contributions by co-modeling both types of RPs in the reliability analysis of multi-state systems with arbitrary structure and heterogeneous system elements. The system performs a primary mission (PM) with the specified time duration. System configuration (i.e., required subset of working elements and system functioning criteria) and reliability characteristics of system elements are different during PM and RP. A probabilistic modeling method is proposed to analyze reliability metrics of the considered system in forms of mission success probability (MSP) and system survival probability (SSP). Based on the MSP and SSP evaluation, two types of mission abort rules (performance constraint-based and system state subset-based) are investigated and compared. An example of an electrical heating system is provided to illustrate the proposed method and solutions to the optimal mission aborting policy that maximizes MSP subject to meeting a certain level of SSP.