What is the subject in a passive infinitive sentence saying "to be considered for a promotion"

The sentence

• They will be offered an opportunity to be considered for a promotion

contains two clauses: a main clause, and an infinitive clause modifying an opportunity. Both clauses have been modified by the Passive construction, among others, and reduced by substitution and deletion rules.

Something like an unwound expansion of this sentence might be

• The company will offer an opportunity to the employees -- (main clause)
  for the company to consider the employees for a promotion. -- (infinitive clause)
  (It doesn't sound like such an opportunity stated that way, does it?)

The company isn't mentioned in the passives, but it's the agent subject of both clauses, in the active.
The clauses are in the passive form because the subject is already mentioned in the preliminary subordinate clause, and because it is obvious from the employee relation mentioned.

• Once the employees have completed the company's largest project successfully,

After this clause, both the company and the employees can be represented by them. The listener is required to understand which one, but since the company is the agent in both clauses, making them agentless passives (applying Passive without the agent by-phrase) gets rid of them. Thereafter, reference to them in this context refers to the employees.

The Passive in the main clause is complicated because it involves Dative,
which is the rule that relates these two sentences, for instance:

• The company offered an opportunity to them.
• The company offered them an opportunity.

Passive applied to these two variants gives two variant of Passive:

• An opportunity was offered to them.
• They were offered an opportunity.

The Dative Passive of the second example is what happens in the main clause.

The infinitive clause loses its original agent subject by agentless Passive,

and then loses its derived for-phrase and the receiver (not agent) subject it introduces

• [for them] to be considered for a promotion

by ordinary infinitive reduction. Most infinitives lack an overt subject, either because the subject is not specific, or because (as here) it is specific, but it can be inferred from the syntax and the context.

Left unanalyzed is the predicative but not syntactic relation between offering an opportunity and its modifying infinitive clause -- the clause details some of the offering and some of the opportunity, and they're related in several ways; but syntactically, all one can say is that the infinitive modifies the noun phrase.