I work as a non billable member in my company. But I complete my tasks assigned to me on time for my project. Is there a chance that in future my company will fire me just because I am non billable?
It's simply a cost code and I wouldn't worry about that, this usually means that the work you do isn't billed to the end customer but is internal only. Individual projects within the company might well have their own cost codes so that they can track use of resources against projects.
Ask your manager or team lead for clarification on what this means for your company and role.
In some other answers I talked about the existence of so-called "bullshit jobs". However I still think that in a lot/the majority of the cases all people who work at a company contribute something essential to it. Nobody is employed just because they are such a nice guy/gal. If the cleaners wouldn't clean the office of your company it would soon become such a mess that people cannot work there anymore. Whatever tasks you are working on are probably needed for the "billable" persons to do their work or is in some other way essential for the company. So the distinction between "billable employees" vs "non-billable employees" and "profit centers" vs "cost centers" is actually hogwash. In most cases all employees do important work that makes it possible for the company to earn money. Personally I think that categorizing some employees as "non-billable" or working in "cost centers" is disrespectful to them.
I mean, they’re not going to just up and fire you for spite for being non billable (unless you work for a purely consulting company in which case they may). But in any organization, when hard times come, the first cuts are always in cost centers, not profit centers. So on the whole, working as a source of cost carries less job security than if you were directly contributing to revenue.
That doesn't mean you're sure to get fired for being in a cost center, but if you are comparing the two in terms of job stability, profit always comes first.
The answer is yes, no, and maybe.
Within some companies tasks can be classified as billable or non-billable. Some employees are almost always billable, or almost always non-billable. Many are a mix.
You see this type of designation when the bulk of the income from the company is through tasks/contracts with a customer. You see this with government contractors. But it can also be done with other types of business. An auto repair shop can only use the time of the mechanics to bring in income. A law office only generates income from the work of lawyers and other similar employees.
In these types of companies everything else needs the billable hours to be maximized to be able to pay their salaries and benefits. This non-billable work is still vital. This non-billable work is still valuable. These jobs can include accountants, sales people, security, warehouse, and management. Of course management has to watch all expenses to be able to pay all the employees, and all the expenses from the billable hours.
Companies that have large percentage non-billable employees can struggle. Each billable employee needs to be 100% billable, or they need to charge a very high rate to fund the rest of the operation. If they need too high of a rate they can lose the ability to when new contracts.
Some tasks being done by highly skilled employees can be non-billable. Some companies have internal teams doing research and development to create new products. These new products can later generate new business, or can be used to allow company employees to be more efficient and therefore generate more income per hour.
Yes it is true that non-billble employees are generally the first things that can be cut if money is tight. But billable employees are also vulnerable to job cuts. If they spend too much time in an overhead state while waiting to be put on a contract, they may find their only option is a change of position or unemployment.
Some employees are mixed. In companies I have work for the first level of management is expected to be moistly billable. The rest of their hours are doing management and business development tasks that the customer won't pay for. As their empire grows their expected billable percentage is reduced. Once they start having mangers working for them they rarely have billable hours. Of course if their empire suffers enough losses in business they may find themselves back to doing billable work.