I will perform periodic diagnostics on the devices remotely and I want to know which parts are not functioning.
By definition there is a simple logical reason this is not possible for anything. It is not possible for your car. It is not possible for the International Space Station, you, your cat, your house, or a Raspberry Pi.
I'll explain this by analogy to the car. Let's say a car manufacturer decides to develop a phone app which allows you to remotely check "which parts are not functioning". Obviously this is possible to an extent. For some things (e.g., proper compression) this may require the car's engine be started remotely. It also obviously requires a complex array of sensors be deployed throughout the car. Depending to what "an extent" we want to go, it may also require the car drive around remotely.
Doing this very thoroughly could add tens of thousands of dollars of cost to the car. What's more, as you add complexity for the remote sensing of non-functioning parts, you increase the potential for the remote diagnostic system itself to malfunction. Having a car drive itself around remotely in order to check if it works properly is not sane.
If sanity is not a concern, you could then set out to spend an infinite amount of time integrating an infinite arrangement of redundant sensors to check the sensors that check the sensors that check the equipment, etc. The further you go down this path, the more absurd it gets, and the less interested consumers are going to be in your car. People do not want a car where millions of R&D dollars have been wasted on a system to check whether or not the car works. They want a car where effort is focused on making sure the car works.
Going back to your actual situation, in comments you have made it clear that what you want to check is not really just a servo, it is, more generally, the state of anything connected to an output that does not have a corresponding input. The answer to this question is:
No, you cannot verify an output is connected to anything without a corresponding input.
However, you can make sure you use appropriate quality components, attach them properly, and do testing and quality assurance on site, before they are shipped out. This may mean hiring skilled staff, etc. There is no magic bullet by which you can overlook poor practices and insufficient resources. If you aren't sure whether something is going to work or not, then you should be honest with the people you are selling it to, or else admit you simply cannot provide what is required.