Applying hydrostatic pressure with suspended 2D material thin membranes allows probing the effects of lateral strain on the ion and fluid transport through nanopores. We demonstrate how both permanent and temporary delamination of 2D materials can be induced by pressure and potential differences between the membrane, causing a strong mechanosensitive modulation of ion transport. Our methodology is based on in situ measurements of ionic current and streaming modulation as the supporting membrane is indented or bulged with pressure. We demonstrate how indirect measurements of fluid transport through delaminated MoS₂ membranes is achieved through monitoring streaming current and potential. This is combined with TEM images of 2D material membranes before and after aqueous measurements, showing temporary delamination during mechanical or electrical stress. The obtained results allow a better understanding of measurements with supported 2D materials, i.e. avoiding misinterpreting measured data, and could be used to probe how the electrical field and fluid flow at the nanoscale influence the adhesion of supported 2D materials.