united-states
Even in the 49 U.S. states that are "employment at will" states in the U.S., there are reasons for which termination of employment is prohibited under both state and federal law, and termination without cause entitles an employee to unemployment benefit if certain other conditions are met.
Most unionized employees, most public sector employees, most private sector employees in Montana, and a small number of employees (mostly senior management) with written employment contracts that so provide can only be fired for cause.
There is a split of authority in the U.S. on the status of not making full disclosure is something that the employer required you to disclose and that you represented that you did disclose in the hiring process, such as your social media accounts. This is commonly called "resume fraud" even though it actually applies more broadly than resumes. Also, sometimes the question might be resolved differently under parallel state and federal laws.
In general, in the U.S., asking about social media accounts is something that an employer may permissibly ask unless it is use to facilitate discrimination on a prohibited ground.
One rule, which applies in some jurisdictions, is that "resume fraud" (i.e. a material misstatement in a resume or employment application) discovered by an employer after an otherwise wrongful termination can serve as a lawful basis for terminating employment that excuses the wrongful basis for termination of employment (at least assuming that the information withheld or misrepresented was on a matter that the employer could lawfully consider). Even if the information not disclosed was not itself a basis upon which the employer would not have hired someone, the dishonestly in the hiring process would be a basis for termination of employment.
For example:
The Seventh Circuit, which covers Indiana, Illinois, and Wisconsin,
has consistently held that it’s permissible for employers to reject
job applicants and fire employees who are suspected of engaging in
resumé fraud. The rationale for the Seventh Circuit’s reasoning is
very straightforward: lying to employers is a legitimate and
non-discriminatory basis for turning down an applicant or firing an
employee. The cases of Carter v. Tennant Co., Aubuchon v. Knauf
Fiberglass and Gilty v. Village of Oak Park all stand for this
proposition. . . . .
If the employer, as part of its investigation of the allegations in
the lawsuit, discovers that the employee engaged in resumé fraud, can
the employer use that belated discovery to its advantage? According
to the United States Supreme Court, the answer is yes. More
specifically, in McKennon v. Nashville Banner Publishing Co., the
Supreme Court essentially held that an employer’s belated discovery of
an independent, alternative basis for firing an employee (e.g., resumé
fraud) can be used by the employer to reduce the plaintiff’s potential
recovery. (Think of this as the employer’s “if we knew then what we
know now, we wouldn’t have hired you in the first place” defense.)
In other jurisdictions, "resume fraud" is not itself a basis for discharge, although it might be used as evidence to support an initially claimed valid reason for terminating employment in the face of an employee allegation that this was a mere pretext for wrongful termination.
I don't know which states or how many U.S. states fall in each category. The former rule is the rule in almost all cases under federal private sector employment law.
A variety of cases that address the question in the context of public employment sector employment can be found here.
In addition to these general rules of law, there are also often reasonable questions of fact about whether a prospective employee substantially complied with an employer's social media disclosure question on a fact by fact basis that turns on the exact wording of the question and the reasonable interpretations that language could be given by the employee.
For example, if a question has a social media disclosure requirement and one doesn't disclose a blog, one might reasonably argue that a blog is not a social media account, depending on the language used in the question.
