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Let's suppose that SIS means "stock incentive share [plan]" and RSUs are Restricted Stock Units. [Am I right? I actually don't know for sure. https://www.lawinsider.com/dictionary/sis-plan  This means you probably work for company A.]

1) Unfortunately your old shares are now selling at a loss. You sell some [say 10 shares] and recognize a loss of $10 per share for a total of $100 capital loss on the sale. 

2) Your company's SIS plan kicks in and you have set your newly vested [10] shares to immediately sell. They do and you would normally have a gain of 0, but...

3) The wash sale rule kicks in since you "bought" [vested RSUs] matching positions of the stock shares you sold at a loss within the window [30 days before and 30 days after the sale at a loss.] This means these new shares get the carryover from the previous loss. https://www.investopedia.com/terms/w/washsale.asp 

a) You no longer show the capital loss on your sale in 1. You now report no loss on that sale for tax purposes. This was the "wash sale."

b) The new [10] shares gets a matching markup in cost representing this undeclared loss of $10 per share on the matching number of [substantially equivalent] shares. "Also, the holding period of the wash sale securities is added to the holding period of the repurchased securities, which increases an investor’s odds of qualifying for the 15% favorable tax rate on long-term capital gains."

c) These shares sell immediately as intended and you again have a [new] loss of $10 per share. You will declare THIS loss on your taxes unless...

d) The same thing happens again a month later, in which case you have to do it all again!

e) The unrelated sale of stock B is unaffected. You report it normally. The wash rules only apply to matching 

4) Moral of the story:

a) This is only a problem with losses. Gains do not trigger "wash sale" rules. So you only have to watch out for it when you are selling shares at a loss in stocks that you are also buying within the window.

b) If a brokerage was reporting both the sales and the purchases for you in the same account, they would hopefully keep track of this, but the brokerage can't know about what happened somewhere else, so you have to keep track of it when it happens in different places. SIS RSUs are a classic example of when the brokerage won't keep track.

c) The wash rule applies even when the sales and purchases happen in different beneficial accounts for the same investor, like your Roth IRA and your taxable brokerage account.

d) While it sounds burdensome, you're not going to have a problem in the long run unless you actually try to use this to avoid paying taxes, which is why the rule was put in place. [I.e., the IRS generally only wants to penalize you if you avoid taxes you should pay, not just because you filled out the forms wrong.]

e) You are going to want to keep the records in a spreadsheet or reconstruct them at tax time, because of the potential to lose track of your proper basis when wash sales are an issue. Of course if you don't do spreadsheets, keeping paper logs of sales and purchases would be a nice thing to hand to your tax preparer, even if that's you as well.