The invention relates to an assembly for a turbomachine, comprising a stator (1) and a rotor (2) rotatable relative to the stator (1) about an axis, the rotor (2) comprising blades each ×comprising a vane (3) connected to a radially inner platform (5), a block of abradable material (6) extending radially inwardly from the radially inner platform (5) the stator (1) having a shroud comprising an annular area (9), at least one lug (12) extending radially outwardly from said annular area (9), the radially outer end of the lug (12) cooperating with the block of abradable material (6).