If a law is struck-down as unconstitutional, but all the precedent
used to find it unconstitutional gets reversed; what becomes of the
law?
In U.S. law, the law has effect again, unless it has been amended or repealed in the meantime.
Is it totally dead, needing be passed anew?
In the U.S., no. It is not totally dead. It is merely dormant. It stays on the books and legislators may decide not to repeal it as a political statement.
It also might be considered for interpretive purposes when construing another part of the same law. For example, the meaning given to a phrase in an unconstitutional part of the law might be applied to a different part of the law that is constitutional.
Can the judiciary be asked to reinstated, after which point it can be
used again?
In the U.S., any court can determine that a law is unconstitutional, but the extent to which that ruling is binding precedent on other courts or other parties than those to the case before it depends upon the court in question and upon the doctrine of collateral estoppel (a.k.a. issue preclusion).
For example, the legal fight in the U.S. to hold bans on same sex marriage to be unconstitutional was fought in and resulted in ruling in dozens of courts at the trial court and state appellate court, and federal intermediate appellate court level before a uniform ruling was established by the U.S. Supreme Court.
Further, even if the issue arises in another case where there is a controlling precedent, attorney ethics permit an attorney to make a good faith argument for a change in the law to any court, so if there is some good faith argument for doing so, the attorney can push that the issue be reconsidered.
Of course, usually the answer from the court will be "no."
Or can it just be enforced again without any formal process; so long
as nobody sues and gets it killed again by a lower court?
Sometimes government officials enforce laws that have been held unconstitutional, either because they aren't aware of the relevant court decisions, or because they think that their facts are distinguishable from those under which the law was held unconstitutional (which sometimes happens on an "as applied" basis rather than on a "facial" basis that applies to all cases), or because they think the judge before them might rule differently despite the precedent.
Also, would the answer differ according to country? If so, could you
please give me some examples of countries handling this differently.
Yes. Many countries with legal systems based upon the legal system of countries of continental Europe like France and Germany and Spain, which are called "civil law" countries have a very different process of handling unconstitutional laws, as does the European Court of Human Rights and the highest court of the European Union.
In Germany, for example, questions of the constitutionality of a law may be raised only in the Constitutional Court and not in other courts. This ruling is usually final. And, unlike U.S. courts, the Constitutional Court can rule a law unconstitutional during the legislative process, rather than in connection with an actual case or controversy relating to the law taking effect (in which case the law never gets on the books in the first place). I don't know what happens when the Constitutional Court declares a law unconstitutional.
I do know, however, that in the case of the European Court of Human Rights and the highest courts of the E.U. that one of the usual remedies will be an order directed at a member state to amend its statutes to remove the offending law, with sanctions imposed if the member state fails to do so. Obviously, once such a law is repealed in this fashion, it would have to be re-enacted to take effect even if the precedent holding that the law was unconstitutional was undermined.