Although rarely heard today, this construction comes down from Old and Middle English, where it was quite common. Because we find it in both our sister and our cousin tongues, it probably originated in a common grandparent, possibly way back in Proto-Indo-European.
In his monumental work An Historical Syntax of the English Language, Volume 1, F.Th. Visser devotes quite a few pages to this construction. On page 858 he writes:
Here the modally marked form is used in attributive clauses. It expresses the speaker’s reserve as to the possibility of the fulfilment of the conditional in the clause. When this reserve is absent, the modally zero form is used.
When Visser says “modally marked form”, he means what most people on ELU mean when they refer to a subjunctive inflection, be it present subjunctive or past subjunctive. When he says “modally zero form”, he means that it is not what you would think of as a subjunctive.
He further writes:
The idiom is extremely common in Old English. In Modern English there are only a few examples, while after the middle of the seventeenth century the usage is obsolete.
He then cites Jespersen opining that in certain common cases it was probably never used at all. Visser also mentions that although French has the same idiom of marking the verb, that it would be rash to look upon the French usage as the origin of the English usage, since the latter was already fully developed in Old English long before the French invasion in 1066.
Some of the citations he provides are:
- What beast couldst thou be, that were not subject to a beast?”
—Timon of Athens, Shakespeare.
- But if to match that Lady they had sought. Another like, that were like faire and bright,...
—Faerie Queen, Spenser.
- Indeed, sir, he that sleeps feels not the tooth-ache: but a man that were to sleep your sleep, and a hangman to help him to bed, I think he would change places with his officer; for, look you, sir, you know not which way you shall go.”
- “...as much may be returned on the Greeks by one who were as witty as himself.”
—Heads of an Answer to Rymer’s Remarks, Dryden.
Here’s another example:
- “If you should see a man, who were to cross from Dover to Calais, run about very busy and solicitous, and trouble himself many weeks before in making provisions for his voyage, would you commend him for a cautious and discreet person, or laugh at him for a timorous and impertinent coxcomb?”
Although Visser relegates this exact scenario to one that he calls obsolete in present-day English, it can be difficult to separate these out from very close scenarios that remain part of the literary register even today.
For example, scholarly texts on mathematics often use were in clauses subordinate to things that ask one to construe a hypothesis to be true, as in suppose that it were.
The point with all these is that some writers use the historical forms to impart a sense of doubt on the subordinate clause. Your initial sentence is doing that when it reads:
It would be unwise for a person who were only a junior in the company to criticise the boss.
That suggests that there is some question about the existence of juniors, or of juniors criticizing bosses. The reason it sounds odd to you is because it is not a common construction in present-day English outside deliberate archaizing texts.
One confusion that some writers have is that additional subordinate clauses do not get marked in the subjunctive:
- It would be better if he were here when Jane was.
Notice Jane takes was there, not were.