If someone had purchased some stocks prior to leaving California, then sold these stocks outside California, do they owe any tax to California?

I believe FTB publication 1031 addresses your question.

The way I am reading it is that if you leave California for good, then you don't have to pay any CA taxes. You only have to pay taxes in state where you were resident at the time of sale.

However, the big question is whether FTB will consider that you have left CA for good. If you remain domiciled in CA (check definition in that publication with few examples), then they still may want to assess taxes on your profits.

For regular brokerage purchases and sales of stocks:

From: State of California FTB Pub. 1031 - 2019 Guidelines for Determining Resident Status

Income Taxable by California

Part-year residents of California are taxed on all income received while a resident and only on income from California sources while a nonresident.

Sale of Stocks and Bonds

The gain or loss from the sale of stocks or bonds has a source where you are a resident at the time of the sale. If buying and selling stocks and bonds is your trade or business, see “Business Income (or Loss)” on page 7 for more information.

Example 15 – You are a resident of Oregon and sell stock of a California corporation at a gain.

Determination: Because you are an Oregon resident, the gain has an Oregon source. The gain is not taxable by California.

Example 16 – You are a resident of California and sell stock of a Kansas corporation at a gain.

Determination: Because you are a California resident, you are taxed on all income, regardless

And: State of California FTB Pub. 1100 Taxation of Nonresidents and Individuals Who Change Residency - Section H Capital Gains and Losses

Part-Year Resident

If you changed your residency during 2009 [example year], compute income and deductions using resident rules for the period of the year you were a California resident and nonresident rules for the period of the year you were a nonresident

So when you purchased doesn't generate a gain/loss event, but when you sold which then "captured" does. Do note that Prorate both capital loss carryover amounts based upon the period of California residency and the period of nonresidency during the year.

I also agree with the other poster that you should confirm your Non-Residency status as described in Pub 1031.