Fifth-generation (5G) and beyond communication systems offer new functionalities and significant performance improvements but that comes at the cost of tougher energy requirements on user devices. Addressing this issue while reducing the environmental impact of the substantial increase in energy consumption can be achieved through energy-neutral systems that operate using energy harvested from radio frequency (RF) transmissions. In this direction, this work examines the concept of utilizing an unconventional source for RF energy harvesting. Specifically, the performance of an RF energy harvesting scheme for multi-user massive multiple-input multiple-output (MIMO) is investigated in the presence of multiple active jammers. The key idea is to exploit the jamming transmissions as an energy source to be harvested by the legitimate users. To this end, the feasibility of this concept is studied via system performance analysis for a training-based massive MIMO encompasses imperfectly estimated channel state information (CSI) at the base-station and employing the time-switching protocol. In particular, the achievable uplink sum rate expressions are derived in closed-form for two different antenna configurations at the base-station. Two optimal time-switching schemes are also proposed based on maximum sum rate and user-fairness criteria. The essential trade-off between the harvested energy and achievable sum rate in time-switching protocol are quantified in closed-form as well. Our analysis reveals that the proposed energy harvesting scheme from jamming signals is viable and can boost massive MIMO uplink performance by exploiting the surrounding RF signals of the jamming attacks for increasing the amount of harvested energy at the served users. Finally, numerical results validate the theoretical analyses and the effectiveness of the derived closed-form expressions through simulations.