If the money came from investments or savings that the student owned, it’s the student’s support. Look at table 2 in IRS publication 501. Lines 1 through 5 address support the student provided themself. It includes looking at the child‘s savings account balances at the beginning and ending of the year, and if you work through a couple of imaginary scenarios, you will see that if the child withdraws money from their own savings account to pay their expenses, that counts as support the child provides themself, but the remaining balance in the savings account is not considered support. There’s no reason to think that an investment account would fall under different rules than a savings account. Money the child spends on themself that comes from their own sources is their own support.
Dependency is determined for each tax year. Suppose the parent gives money to the student in 2021, which of the student puts into a savings account. It becomes the student’s own money. Suppose the student then withdraws the money in 2021, a few days or weeks later perhaps, to spend on tuition or rent or other support. I think it is not correct to consider this money that the student provided themself, because it is clearly money provided by the parents, even if it made a brief stopover in the child‘s bank account. (We can also look to the IRS view on substance over form.)
Now, suppose the parent gives money to the student in 2021 which the student puts in their savings account. Then in 2022, the student withdraws the money to pay for tuition, rent, or other living expenses, but the parent provides no additional funds in 2022. Since the student paid their 2022 living expenses from their own funds and the parent provided nothing in 2022, the child would not be a dependent in 2022.
