Virial theorem for two particle inelastic collision

Consider two point masses separated by a large distance R so that their initial potential energy can be considered 0. They are both at rest with respect to the Centre of Mass (COM) reference frame so that the total initial kinetic energy is also 0 and hence the total initial mechanical energy is 0.

Assuming no net external force on this system of particles except their mutual gravitational interaction, the particles start accelerating towards each other at $t=0$ and collide inelastically at $t=T$.

Since the collision is inelastic, the particles stay put at the centre of mass for all $t>T$.

For all $t>T$, the kinetic energy of both particles just before collision has been converted to internal energy of the particles after the inelastic collision.

However, the virial theorem states that the kinetic energy is half the potential energy in this case. Which is clearly not the case in the situation described above. Can you please help locate any errors in my argument?