In general a deduction is only good if you are itemizing, unless it is a deduction that you are allowed to take even if you take the standard deduction. Items that fall into this category are a $250 teacher deduct om for supplies, and the $300/$600 charitable donation since 2020.
Assuming you can see the impact of the deduction on your tax forms then the amount it saves you in taxes is your marginal rate times the amount of the deduction. If you are in the 10% tax bracket then a $1,000 in extra deductions saves you $100. If you are in the 32% bracket it will save you $320.
In these calculations don't forget your state and local income taxes. In some cases the list of things that are deductible are different. In some states the decision to itemize or not must match between the federal and the state taxes. In other cases, you can itemize on one and take the standard deduction on the other.
In some cases the government doesn't allow a deduction, instead they give you a tax credit. That saves you $x no matter your income, assuming that you qualify for it. Those economic stimulus payments the last few years were tax credits. The best tax credits are refundable. In those cases you can essentially have a negative amount of taxes.
I assume that if a person's taxable income is at $0 for the year then
there's no benefit to keep searching for write offs. Is this the case?
So if by write-off you mean deduction, then once you get to zero there is no benefit. But if you mean tax credit, then it is possible to get that credit paid to you even if you taxable income was zero.
There are a small number of cases where if you can't use the full deduction, it can be rolled over.
This is an area where the tax software packages do a good job. List everything that applies, and see what the result is.
Furthermore, if you have 50k taxable income then a write-off of $1000
is more advantageous (in theory) than if your taxable income is 5k. Is
that correct?
If your taxable income is $5,000 then finding another $1,000 to deduct will save you $100, which you can see as a 2% bump in pay. If you have $50K in taxable income then the $220 you save is like a 0.44% bump in pay. It's all relative.