'As can be seen ...' <--- Can English have a tensed clause without a Subject?

Solution 1:

(1) As ____ can be seen from the figures, the number of first year students decreased dramatically in the last five years.

The gap '_____' in (1) is there to show that the subject is missing, and that As is not the subject. Before addressing why and how a subject is omitted from a tensed clause, I'd like to first prove that As is not the subject.

Why is it that As is not the subject?

There are at least two arguments that could easily be made against calling "as" a relative pronoun or even a pronoun.

(A) The entire as-clause is "mobile" (as @BillJ correctly commented):

Thus, sentence (1) means the same thing as these sentences:

(2) The number of first year students, as ____ can be seen from the figures, decreased dramatically in the last five years.

(3) The number of first year students decreased dramatically in the last five years, as ____ can be seen from the figures.

In contrast, a relative clause can only be used after its antecedent; therefore, the following sentence doesn't work:

(1') *Which can be seen from the figures, the number of first year students decreased dramatically in the last five years.

Adding the relative clause right after the subject is possible, but the relative pronoun does not refer to the same thing as the gap '_____' refers to in (2).

(2') The number of first year students, which can be seen from the figures, decreased dramatically in the last five years.

(Note here that there's no gap in the relative clause, because which is the subject of the relative clause, and that which here corresponds to the gap in (2).)

Here, which refers to the noun phrase (The number of first year students), but the gap '_____' in (2) refers to the entire main clause (The number of first year students decreased dramatically in the last five years).

Now, adding the relative clause at the end is also possible:

(3') The number of first year students decreased dramatically in the last five years, which can be seen from the figures.

At first glance, (3) and (3') seem to mean the same thing, but they actually don't. In (3) the as-clause is used to confirm what is already known, whereas in (3') the relative clause is used to introduce new information.

This is why (4) doesn't work whereas (4') does:

(4) *The number of first year students decreased dramatically in the last five years, as shows that our student recruitment strategies need revising.

(4') The number of first year students decreased dramatically in the last five years, which shows that our student recruitment strategies need revising.

(B) Auxiliary verbs can be can be omitted as well as the subject from the as-clause (no pun intended):

(1'') As _____ seen from the figures, the number of first year students decreased dramatically in the last five years.

(2'') The number of first year students, as _____ seen from the figures, decreased dramatically in the last five years.

(3'') The number of first year students decreased dramatically in the last five years, as _____ seen from the figures.

Here, the gap is not just the subject but the subject and can be. Although the meaning of these sentences is slightly different from that of (1)-(3), the omission of can be is entirely possible or even preferable, as shown in this Ngram.

This omission is impossible in (2') or (3'), because a relative clause has to be a finite clause.

Why and how is a subject omitted from a tensed clause?

From the second argument above, we now know that not only the subject but also the subject and auxiliary verbs can be omitted. So it's not a case of omitting a subject but rather a case of omitting anything that's unnecessary in a subordinate clause. In the OP, what's unnecessary just happens to be the subject of a subordinate clause, specifically a comparative clause.

Generally, a subject and any other complement of a tensed verb can be omitted in a subordinate clause such as a relative clause and a comparative clause. It's only in the content clause that a subject cannot be omitted.

Solution 2:

Dictionary.com gives a few pronoun senses for as, including this one:

14. a fact that:
    She did her job well, as can be proved from the records.

As functions analogously to relative pronouns like which, that, and who; it serves the dual function of pronoun and subordinator.

Inserting it would completely change the meaning.