First to answer your question, when you go to Malaysia, and go back to Singapore, you might get a regular tourist pass. Or you might be denied entry altogether.
What you are attempting is a visa run, which works in countries like Thailand but not so much in Singapore, where that practice is frown upon.
Before she came, she had to file an "SG Arrival Card & Health Declaration". Then she received an acknowledgement, stating she was getting 90 days. She also had to mention her date of departure. If that date has already passed, ie her flight was well before the 90-day mark, there will already be a suspicion of deception. She received before arriving a reminder by email to update the declaration if there were changes to her travel plans.
Now if the extension is refused, which is possible, even probable, she will have to leave by day 90. She would have, while in Malaysia, to submit another SG Arrival Card & Health Declaration. And considering there will be her record of her applying for an extension, on top of the 90 days spent in Singapore, that might even get denied. Or later, in Singapore. If ICA flags her passport, and she's redirected to a manned counter, she'll be asked about why she's used up all 90 days, and did a visa run. She might be denied altogether, and sent back to Malaysia, or given a visa for just a few days, enough to get her plane ticket sorted out.
There used to be a social pass or something like that, which allows a visitor to stay up to one year. Not sure it still exists, but if it does, that's what she should apply for. Next time. For now, make sure she goes back home within the 90-day limit. You'll save her a lot of hassle.