What approach would an algo trader use if the previously stable spread on ETF ABC widens against ETF XYZ from ABC becoming more valuable versus XYZ?

I have an issue with the Algo answer but before I get to that, if the B/A spread widens, you have more to overcome just to break even on a position. In addition, you can't profitably pairs trade based on the B/A spread width because there's no meat there.

I have no idea what the lingo of the Algo class is so here's my take from having profitably traded an awful lot of pairs in every major volatile time period since 2008. You sell the overvalued security and you buy the undervalued security.

Something doesn't add up here (the question and their answer) so I'll leave it to you to figure out exactly what the Algo class is suggesting. Based on the wording of your question, I would buy XYZ because it's undervalued and short ABC because it's overvalued.

Here's an article about pairs.

"spread" in this context is just the difference between the two ETFs (not B/A spread). Typically it's used to measure against some benchmark, but it can be used against two arbitrary instruments.

However, the answer seems backwards to the question. If one expects the spread between ABC and XYZ to close (meaning that ABC - XYZ gets smaller) then one would go SHORT ABC and LONG XYZ, not the other way around.

The answer does make sense if ABC trades for less than XYZ, in which case the "spread" is negative and you'd make the trades outlined in the answer (since ABC would gain relative to XYZ), but that detail is left out of the question as posted.