If you want to retain the future continuous in the passive transformation, you can use "getting" instead of "being":

My clothes will be getting washed by my mother.

"will be being" is a combination a speaker of American English is not likely to hear in a lifetime.

Although this question is more fit for ELL but I'll try to explain.

Active

Active voice describes a sentence where the subject performs the action stated by the verb.

For example:

John washed the dishes two hours ago.

Let's break it down:

• Subject: John
• Verb: washed (past)
• Object: the dishes

Therefore in active voice, you always have a subject (John) that is performing an action (Washing the dishes).

Passive

In passive voice sentences, the subject is acted upon by the verb.

Same example in passive voice:

The dishes were washed two hours ago.

Again breaking it down:

• Subject: The dishes
• Verb: were washed (passive past)

So as you see, in the passive voice, washing (verb) is acted upon the dishes (subject). By who? We don't know/care.

Active vs Passive voice? (When do we use them)

Usually, when the action itself is more important than the doer of the action, you use passive form.

Another situation would be, if you don't know who did an action or you don't care who did it, then you use passive.

So for example, When I say "The dishes were washed two hours ago.", I'm not saying who did it. Maybe because I actually don't know who did that, or maybe I don't care. Or maybe it's because it's not important who did it, the important thing is that they are washed.

In other situations, Active is usually preferred.

As stated by @Lynn in this answer, please keep in mind that:

In many styles of writing, active voice is preferred over passive voice for clarity and easier reading. However, in other styles of writing (particularly technical/legalese, which it sounds like you're quoting from), the more stilted sound of passive voice is more common - and perhaps even preferred.

Original Example:

You're (corrected) original line was:

If i run a test on my PC (I am a software tester) and it gets failed fails

Then you asked if you should say

• My test is failing

"My test is failing" is a correct active sentence although its tense is not quite right. To fix the tense, you should instead say: "My test has failed." or "My test failed". (because it happened in the past)

For instance:

My test has failed because of a programming bug.

It's still active because as mentioned before, you have a subject (My test) that is doing something (failing).

• My test is being failed

This is not a correct passive voice. If you want to say it passively, you should instead say: "My test is failed". But it still sounds unusual. In this particular example, I'd use the active voice for clarity. You could definitely say something (passive) like:

If my test is failed, then...

But the active form is more clear and is preferred

If my test fails, then...

Conclusion

Use active for this particular example but as the rule of thumb, if you don't know when to use Active and when to use Passive, ask yourself which one is more significant. If the doer of the action is more important use active or if the action itself is more important, use passive.