Briggs used two different style fuel pickup systems for carb with side mounted pump used on your eng.One system had a single pickup tube either brass/plastic with a filter screen on bottom of same,some of these had a ball check valve in tube above screen,if screen damaged/missing ball in bottom of tank may be from tube,in which case pickup tube assembly will have to be replaced.
The second system is a two pipe pickup(1 long,1 short)pickups may be brass/plastic each with a filter screen & possibly a check ball in one/both pipes,in this system the tank has a reserve well welded into top of tank that short tube goes into when carb is mounted on tank,if ball you're talking about is in this well,then it might be check ball from pickup tube,in operation pump pulls gas from tank thru long tube & pumps into well,short pickup pulls gas from well to feed main jet in carb,any excess gas from pump just overflows back into tank after well full.
Another thing to check,remove cover from fuel pump & confirm that pump return spring/cap are installed in cavity in carb BODY side of pump diaphram and NOT in cavity of pump cover(easy to do,been there done it)also while pump apart check that vac passage between pump body & carb venturi not plugged/gummed up,run a fine wire thru same then blow out with compressed air.Check that pump body not warped or pump cover not warped allowing pump to suck air.
Also check brass/plastic tubes for splits/cracks & also that tube(s) are tight in carb body.
You might want to pickup a service/repair manual(pn270962) for your eng from local dealer,briggs website or ebay,manual will have service instructions for both types of carbs.