My parent has a large capital loss carryover ($1 million) from his stock investments. My own stock investments currently has an unrealized gain of $300,000. If I gifted my appreciated stock to my parent who then sells it, would his capital loss carryover offset the $300,000 capital gain from the sale of the stock and therefore owe no taxes on it?
No. Even if you gifted it, if they sold it within a year the recipient would be taxed at the higher, short term capital gains rate. It would have no relation to other long term investments already in the portfolio of the recipient.
If you gift your parents your appreciated stock, their basis in the stock will be equal to your adjusted basis for calculating a gain. Also, their holding period will include your holding period. Therefore, if your parents sell the stock after you gift it to them, they will recognize a long-term gain--assuming you held the stock for more than a year--of $300,000. If they have a capital loss carryover of $1,000,000 from prior tax years, that will offset the gain from the sale of the gifted stock. In other words, yes they will not owe tax on the gain.
Please note that you will have to file a gift tax return (Form 709), since the fair market value (FMV) of this gift exceeds the annual exclusion of $15,000. However, you most likely will not owe any gift tax. There is a lifetime exclusion of $11.18M, which means you can gift up to that amount during your lifetime without any having to pay any gift tax. That lifetime exemption is also used for determining your taxable estate upon death, so if you have a significant estate, this gift might impact your estate tax plan.
Keep in mind that, if this is a tax avoidance scheme, meaning the intent is for your father to give you back any of the proceeds from the sale, the IRS would find this to be an attempt at fraud and would undo the transactions and change you some penalties.