For an electronic load product type like the 2380 series, you are right to be aware of minimum operating voltage when sinking current.
However, a SourceMeter has very different analog architecture and does not have a similar concern.
If asking the SMU to source negative current (sink current into the HI terminal) you will also specify a (maximum) voltage compliance limit. But the actual voltage that will develop between the HI to LO terminal is a consequence of the I*R drop external to the SMU and not due to internal I*R drops.
You could short HI to LO and have it sink current and it would be perfectly happy with the near to zero volt drop on HI to LO.
When sourcing current, the minimum allowed voltage compliance programmed value is 10mV. But you'd set it this low only if you wanted to enforce this as a maximum voltage that the DUT should experience when forcing the current by the SMU.
Instead, you would set the voltage compliance to value larger than the expected I*R of the DUT.