The House of Judah is already cut off from the Spiritual Tree. Like everyone, it is only by accepting Jesus, that Jew and gentile can be grafted in.
The basic problem of who is Israel, is coloured by the false 'rapture' of the Church to heaven, before any turbulation. For this wrong theory to work, there must be an Israel on earth undergoing the great Trib. This belief then has the Jews mass converted when Jesus Returns.
That this whole scenario is false and impossible, is easily proved by careful study of all the Prophesies.
The house of Judah has never been cut off. Your assertion ignores everything Paul said about the remnant. The remnant of the house of Judah is the reason why the nation continued to exist (was not cut off) and it's into this nation that Gentiles who believe in Christ have been grafted.
Together the Jews and Gentiles in Christ are the citizens of Israel who are living stones making up a Temple - the New Testament Temple of God which did not REPLACE the nation of Israel - but since the citizens ARE now the Temple, in the New Covenant the (citizens of) the nation (Israel) and the Temple of God are the same thing. In the Old Covenant the nation and the Temple were not one and the same thing.
And THE ABOVE nation is STILL the house of Judah - the foundations of its Temple are the
Jewish apostles and its cornerstone is the
Jewish Messiah - and it's the nation which since 722 B.C is also called "the whole house of Israel" - because through the remnant the house of Judah / "the whole house of Israel" continued to exist.
The northern ten tribes are never called
Israel, the house of Israel or the whole house of Israel IN SCRIPTURE
after BC722 - but
the house of Judah continued to be called
Israel, the house of Israel or the whole house of Israel IN SCRIPTURE
after BC722. Nor did the house of Israel or the house of Judah cease to exist AFTER CIRCA AD30. God kept for Himself a remnant.
There would have been no elect nation for Gentiles to be grafted into if the house of Judah was cut off. But the majority were cut off. The remnant remained.