T-lymphocytes in the human body routinely undergo large deformations, both passively, when going through narrow capillaries, and actively, when transmigrating across endothelial cells or squeezing through tissue. We investigate physical factors that enable and limit such deformations and explore how passive and active deformations may differ. Employing micropipette aspiration to mimic squeezing through narrow capillaries, we find that T-lymphocytes maintain a constant volume while they increase their apparent membrane surface area upon aspiration. Human resting T-lymphocytes, T-lymphoblasts, and the leukemic Jurkat T-cells all exhibit membrane rupture above a critical membrane area expansion that is independent of either micropipette size or aspiration pressure. The unfolded membrane matches the excess membrane contained in microvilli and membrane folds, as determined using scanning electron microscopy. In contrast, during transendothelial migration, a form of active deformation, we find that the membrane surface exceeds by a factor of two the amount of membrane stored in microvilli and folds. These results suggest that internal membrane reservoirs need to be recruited, possibly through exocytosis, for large active deformations to occur.