Which compound results in the following products when mixed with AgNO3 and Chlorinated water
The black precipitate can either be


metallic silver, formed by reduction of the $\ce{Ag+}$ ions (most likely)
an insoluble silver salt


Possible candidates for the sodium salt:

╔══════════════════╦═══╦═══╗
║      SALT        ║ 1 ║ 2 ║ 
╠══════════════════╬═══╬═══╣ 
║Sodium bisulfate  ║   ║   ║ 
║Sodium borate     ║   ║ ? ║ 
║Sodium citrate    ║   ║   ║ 
║Sodium chloride   ║   ║   ║ 
║Sodium fluoride   ║   ║   ║
║Sodium nitrate    ║   ║   ║
║Sodium nitrite    ║   ║   ║
║Sodium oxalate    ║   ║   ║
║Sodium sulfate    ║   ║   ║
║Sodium sulfite    ║ ✔ ║   ║
║Sodium thiosulfate║ ✔ ║   ║
╚══════════════════╩═══╩═══╝


The reaction with chlorinated water tends to show it is the first case (maybe with sodium thiosulfate).

Regarding the pungent odor, $\ce{H2S}$ has a strong rotten-egg odor.

A specific test for sodium thiosulfate is adding an acid (such as $\ce{HCl}$ to the unknown salt solution). A yellowish-white sulfur colloid should slowly appear.

A specific test for sodium sulfite is the decoloration of fuschine (should be available in a microbiology lab): add a buffer at pH = 7 to 1 mL of your unknown salt solution, then 1 mL of fuschine. After a few seconds, it should turn transparent.

Can you conduct those test to get more insight on this? If the first one is positive, no need to do the second one.