Normally when a person gets in trouble with the law it's about a law that could apply to anyone: murder, theft, etc. Is there a name for a law that's against a specific person instead of the crime?
Bill of attainder
This is how conviction by legislation is termed in English legal history. The practice is now effectively redundant and is generally viewed as odious, against the basic principles of justice and a fundamental violation of a proper separation of powers for government. For most of the time the practice was current, the English and Welsh Parliament in Westminster and the (English) Parliament of (some of) Ireland were the only legislatures operating in the English legal framework and tradition, and both passed bills of attainder at various times.
According to Wikipedia:
A bill of attainder (also known as an act of attainder or writ of attainder or bill of pains and penalties) is an act of a legislature declaring a person or group of persons guilty of some crime and punishing them, often without a trial.
Although in modern usage a bill is legislation which has not yet been passed - not yet an act or a statute - this somewhat confusing phrasing is the most common form today, and, probably not coincidentally, is the version which is used in the US Constitution, where enacting bills of attainder is specifically prohibited to both the federal and state legislatures:1
No Bill of Attainder or ex post facto Law shall be passed [by Congress].
No State shall... pass any Bill of Attainder, ex post facto Law...
Although the very idea of the legislature voting a conviction and sentence on someone strikes against our basic ideas of fairness, bills of attainder were at times used as a legitimising (or, at least, legalising) tactic by monarchs who did not want to be seen to be murdering the more powerful of their opponents and plundering their surviving families in most arbitrary caprice - much better that their enemies be hung out to dry with the parliamentary seal of approval.
Some vestige or loose parallel of the bill of attainder can perhaps be seen in the US Constitution in its procedures for impeachment and trial of the president by Congress, and in other constitutions influenced by the US model, such as the Constitution of Ireland, which has similar provisions for impeachment and removal of the president by the Irish legislature - provisions that have, thus far, never been used.
(From a legal history point of view, impeachment is also almost an answer to this question, as it was the first part of another historical procedure of the Westminster parliament by which the legislature tried and convicted an individual by vote. An individual could be 'indicted' (impeached) by the Commons prior to a trial by the Lords. Unlike a bill of attainder (or any other bill), impeachment did not require the royal assent and so was a weapon employed by Parliament in its power struggles with the monarch.)2
Etymology of attainder
Bills of attainder were political weapons, typically aimed against the enemies of the Crown; treason invariably figured on the charge sheet. Attainder itself refers to the loss of rank, rights and realty that came with a very serious criminal sentence such as treason.
Oxford Living Dictionaries carries the following definition:
The forfeiture of land and civil rights suffered as a consequence of a sentence of death for treason or felony.3
(Loss of life was, of course, a very likely consequence too. However, attainder and the seizures it entails can be carried out in absentia, unlike execution.)
With this definition in mind it is easy to understand why one of the basic meanings of attainder, originally a verb, was seize:
mid-15c., in law, "extinction of rights of a person sentenced to death or outlawry," from noun use of Old French ataindre "to touch upon; strike, hit; seize; accuse, condemn" (see attain).
For use of French infinitives as nouns, especially in legal language, see waiver.4
Although attainder does not derive from taint, as one might suspect at first glance, they are indeed related. Taint is perhaps attainder's bastard child:
1570s, "to corrupt, contaminate," also "to touch, tinge, imbue slightly" (1590s), from Middle English teynten "to convict, prove guilty" (late 14c.), partly from Old French ataint, past participle of ataindre "to touch upon, seize" (see attainder).
Also from Anglo-French teinter "to color, dye" (early 15c.), from Old French teint (12c.), past participle of teindre "to dye, color," from Latin tingere (see tincture).
Related: Tainted; tainting.5
Both these word origin excerpts are from the Online Etymology Dictionary.