Telerehabilitation and robotics, either traditional rigid or soft, have been extensively studied and used to improve hand functionality after a stroke. However, a limited number of devices combined these two technologies to such a level of maturity that was possible to use them at the patients' home, unsupervised. Here we present a novel investigation that demonstrates the feasibility of a system that integrates a soft inflatable robotic glove, a cloud-connected software interface, and a telerehabilitation therapy. Ten chronic moderate-to-severe stroke survivors independently used the system at their home for 4weeks, following a software-led therapy and being in touch with occupational therapists. Data from the therapy, including automatic assessments by the robot, were available to the occupational therapists in real-time, thanks to the cloud-connected capability of the system. The participants used the system intensively (about five times more movements per session than the standard care) for a total of more than 8hr of therapy on average. We were able to observe improvements in standard clinical metrics (FMA +3.9±4.0, p<.05, COPM-P+2.5±1.3, p<.05, COPM-S+2.6±1.9, p<.05, MAL-AOU +6.6±6.5, p<.05) and range of motion (+88%) at the end of the intervention. Despite being small, these improvements sustained at follow-up, 2weeks after the end of the therapy. These promising results pave the way toward further investigation for the deployment of combined soft robotic/telerehabilitive systems at-home for autonomous usage for stroke rehabilitation.