here's an explanation.   as self-employed or partner in a business not involved exempt activities the taxpayer's net earnings up to about $149,000 (the earnings are then multiplied by .9235 resulting in a max of $137,700 for 2020 that are subject to fica taxes of 12.4%. in addition, all these earnings are subject to a medicare tax of 2.9%. I won't get into situations when the medicare tax can be higher.  in an S-corp the wages the shareholders take are subject to the same taxes but half comes out of the s/h w-2 and 1/2 is paid by the corp.  the key here is that any remaining profits are taxed to the shareholders but they do not pay the fica or medicare tax on them.

so, in theory, if the shareholder took no salary they would not pay these taxes and while their taxable income would go up by the taxes the S-corp doesn't pay (over $10,000 on a $137,700 salary), the increase in income taxes might be a max of 50% of this amount thus saving over $5,000 + the shareholder saves over $10,000 in the taxes not taken out of their paycheck.   however, the IRS strongly frowns on this and a taxpayer avoiding taking a reasonable salary faces substantial additional taxes, penalties and interest. 

there is an offset to this. as a sole proprietor or partner, all their net income may qualify for the $20% QBI deduction. .However, for most S-corp shareholders only the 20% net income from the S-Corp qualifies. their salary doesn't.