There is a simple answer to your question, and a complicated answer.
Simple Answer: Yes. She can do either.
Basically, if she has lost money on the commercial annuity (CA), and wants to switch from that CA to a CGA with your charity, she should sell the CA and use the proceeds to fund a CGA. However, if she has made money of the CA she should "trade it in" on the CGA by donating the CA to you in exchange for a CGA.
Now for the complicated part, also known as "the Devil's in the details":
There are dozens of types of CAs on the market, and each accumulates and counts gains and losses differently. Also, each company has different regulations about who/when/how to cash in the annuity. In some cases the owner may not be able to donate the annuity to you. In some cases it may be allowed, but the hassle related to getting the company to give your charity the money might not be worth it.
A qualified professional needs to look at the actual contract and the most recent statement. If she has an advisor or accountant who usually prepares her taxes, that person is probably the best-qualified individual to give the most informed and balanced opinion about whether she should sell the CA or donate it to you. Since there are probably more CAs that show losses than gains right now, it would probably make more sense for her to sell the CA, take the losses, and donate cash to fund a CGA. However, she may face stiff penalties, which also vary widely between types of CAs and companies that sell them. There are other tax issues which her tax advisor will be better qualified to address than either you or me.
Also, it's important to realize that if she paid $50,000 for a CA and it's now worth $40,000, she may not have any "losses," since she may have received a cash stream for several years that is calculated (at least partially) as a return of her principal.
So, I'd suggest a variation on the planned giving professional's standard approach of asking her to seek professional advice before acting. In this case, I would advise her to show both the CGA quote you prepare and the CA contract and statement to her tax advisor and strongly suggest that she ask his advice about her next step. I would add strong language that states that you are not able to make any specific recommendation about her commercial annuity (CA).