It's the norm. Most startups offer market salary + stock options. Most of my friends who took significant salary cut for stock options got burned. I have no idea how much salary and equity is being offered to you, but here is an example.
Consider this, most likely the startup will fail and your equity will be worth zero. You need to evaluate risk & sacrifice vs opportunity.
Let's assume that this startup will get acquired for $50 million after 5 years and 3 rounds of funding. You take a 50% salary cut and 1% stock options; which will be diluted to about 0.25% after 3 rounds of funding (depending upon investment terms). You will get $125,000 (0.25% x $5 million) after 5 years. Is it worth the salary cut and sacrifice you will make?
There is a very little chance that this startup may turn out to be a $1 billion exit. Let's assume this happens after 10 years and 8 rounds of funding. At this point, your 1% equity is diluted to about 0.04%; so you will get about $400,000.
If the startup is acquired for anything less than $50 million, you will probably not get anything.
If I were to join a pre-funding startup and take significant salary cut, I would expect at least 10% equity.