The ever-increasing supercomputer architectural complexity emphasizes the need for high-level parallel programming paradigms. Among such paradigms, task-based programming manages to abstract away much of the architecture complexity while efficiently meeting the performance challenge, even at large scale. Dynamic run-time systems are typically used to execute task-based applications, to schedule computation resource usage and memory allocations. While computation scheduling has been well studied, the dynamic management of memory resource subscription inside such run-times has however been little explored. This paper studies the cooperation between a task-based distributed application code and a run-time system engine to control the memory subscription levels throughout the execution. We show that the task paradigm allows to control the memory footprint of the application by throttling the task submission flow rate, striking a compromise between the performance benefits of anticipative task submission and the resulting memory consumption. We illustrate the benefits of our contribution on a compressed dense linear algebra distributed application.