Why the DMM (multimeter) register negative resistance when measure a drop of hydrochloric acid
The multimeter probe tips are dissolving and setting up a galvanic cell that augments the current flow thru the ohmmeter. 
The probe tips may be of the same metal, but the ohmmeter voltage will favor the dissolution of one over the other, and the cell thus formed will assist the applied voltage.
Quickly switching to voltmeter (or milliammeter) mode will show a cell voltage (current).
Using the ohmmeter to measure resistance of a non-corrosive solution (e.g., NaHCO3) will show some (positive) resistance.
Inert electrodes (Pt, Au) will show a positive resistance.