Perhaps you have an elderly relative or friend who is now in a small apartment or assisted living. It's often important or preferred to keep her volume of "things" down and footprint minimal. Although sending fruit supports this objective, there is a risk to consider.
It is so common to send fruit on certain holidays and for some types of celebrations, like birthdays.
If it's going to a large or young, health conscious family that likes fruit, you have a good chance of it being enjoyed and used just as long as not too many others are sending the same thing.
In the case of it going to one person, like an aunt, mom or a grandma, the probability that it will get eaten drops significantly, particularly when others are also thinking about sending fruit. If this happens (and it often can, particularly with big holidays or important celebrations), there is no way all of the fruit will get eaten by this one person. And you may be lucky if it ends up being taken to a shelter or food pantry before it becomes too ripe or rotten.
You should also think about the possibility that she would like something that she can keep more than a week. There are alternatives to sending fruit which don't take up a lot of space. Perhaps this person is in a nursing home or in assisted living or just plain has too much "stuff". The idea of getting something perishable isn't bad because of this. The problem is that there may be a good chance it won't get used. So, even though it will be removed from the living space in a short period of time, in this case, it may not be eaten and enjoyed.
If you are open doing something other than sending fruit this year, keep in mind that sentimental women sometimes like something they can hold or look at to remind them of you and your thoughtfulness! And, if she really doesn't tend to buy nice things for herself, something to consider is a well made silk scarf in time-tested colors and a timeless design. Otherwise, you may want to consider some wonderful bees wax candles or fragrant triple milled soap.
Regardless of the way you go, make sure you give some attention to the gift delivery and presentation. It can be just as important as the gift itself! It helps the recipient to get excited about receiving a gift and to also become filled with wonder about what the gift might actually be.