This paper investigates a control structure to enhance the DC fault ride-through capability of a full-bridge modular multilevel converter (MMC) station, while ensuring a stable controlled operation as a STATCOM during DC faults without the need for fault isolation. Taking advantage of the switching states of a full-bridge submodule, a DC current controller is proposed, which provides the DC voltage reference for the modulation when a DC fault is detected. By changing the outer controllers strategy from DC voltage or active power control to converter energy control during a fault, the decoupling of the converter operation from the DC side dynamics is realized. In this paper, the focus is on the control methodology at all times of operation and the evaluation of the STATCOM control during a fault. To this end, extensive simulations were performed on a three-terminal high voltage direct current (HVDC) grid in radial configuration and a pole-to-pole DC fault case was investigated. The results showed that the AC voltage and current were controlled within limits at all times, while the full-bridge MMC was able to provide reactive power support to the AC grid. Moreover, using the proposed control methodology, the transients at the operation transition points between STATCOM and inverter/rectifier operation were minimized and the stations were able to safely ride through the fault.