The motor torque production can be though of as having a direct relationship to the ratio of voltage and frequency that the motor was designed for. So if you maintain that ratio, you can create full load torque that the motor was designed to deliver. So for example a 460V 60Hz designed motor will produce FLT at any point where the ratio of V/Hz is 7.67:1, which is 460/60. So if you want FLT from a motor that is turning at 1Hz, you give it 7.67V, at 10Hz you give it 76.67V. This is essentially what a VFD does for you.
A little higher than that ratio and you can get Break Down Torque, based on the ratio of the current expected at BDT, which because once you are at that point, is going to be synonymous with current. So if your motor is capable of 225% FLT as BDT, then the current to get to BDT will be 225% of what is would be at FLT, with commensurate heating effects. That means the V/Hz ratio will be 17.25 V/Hz, so again at 1hz you give it 17.25V, at 5Hz you give it 86.25V etc. etc. At low speeds, the ability to do this accurately with all of the varying electrical equivalent circuit interactions going on gets more and more difficult with simplistic V/Hz drives, but that's where a "Vector Control" capable drive comes in to play. By being able to slice the "pie" of current going to the motor into smaller and smaller units of measure, a Vector Drive can effectively separate out the current vectors that produce torque vs the current vectors that produce flux, and maximize the torque production by only fluxing the motor as much as is absolutely necessary. So in essence, more of the total current going to the motor is producing torque when a Vector Control algorithm is used.
At that extreme low end there are also losses to contend with based on that issue of flux producing current as well, because although the majority of the circuit losses are based on the current through the windings or the load on them, there are some, about 25% of the total losses, that are fixed. As the overall power consumed by the motor and load gets smaller and smaller, those fixed losses begin to represent a larger PORTION of the energy consumed, which does show up as current, and therefor additional heat (in relation to the work performed). How much that is depends a lot on the motor design, but is usually reflected in the efficiency rating of the motor. This is why, to be accurate, a Vector Drive must establish and maintain a mathematical equivalency circuit for the motor connected to it, which is what is done in a "tuning" procedure at commissioning.