The stuff left behind, usually called trub. Should not adversely effect your original gravity. That volume of stuff has various solids mixed with your wort, but the liquid part of it is similar to what you drained off the top.
Taking a hydrometer sample after yeast addition (but before active fermentation) should also not reduce the OG or throw it off at all. If you poured a large starter in, that can reduce the original wort’s OG - but that is something that can be calculated and shouldn’t result in a 1.020 or more reduction.
Adding sugar will raise your OG. It is about 1.009 points per pound in a 5 gallon batch. However, table sugar and corn sugar are nearly full fermentable by beer yeast. The result is that you will raise the ABV, and the beer will seemingly dry out as it will finish at the same finishing gravity as the beer before the addition. Your originally planned OG of 1.086 might have finished at an estimated 1.022 (guesstimate). Your 1.060 beer may go down to 1.014. If you add 2.5 lbs of sugar, the OG gets near 1.086, but may still finish around 1.014 because of the fermentability of sugar. Rather than worry about math, the point is that sugar does not make up for the lost OG without other impacts.
Some styles favor sugar additions (many Belgian styles and double IPAs), but there are recipes that give guidance on amounts. A single pound is often used in 5 gallons but some use more.
I would not advise adding sugar unless you are OK with the resulting impacting of higher ABV with a thinner, dry-tasting result. If you do decide to, I’d use restraint.
It’s better to figure out why the miss and dial it in better next time.
Sent from my iPhone using Tapatalk