All perfect praise be to Allah, The Lord of The Worlds; and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
The pillars of Umrah are: Ihram, Tawaf, Sa`y and Tahallul (lifting the restrictions of Ihram). One who fails to offer any of these pillars remains in a state of Ihram until he/she offers it.
One who went back to his country without having offered all the pillars of his Umrah is considered in a state of Ihram and he is obliged to go back to Makkah and finish his Umrah.
While in a state of Ihram, he isn`t allowed to violate any of the restrictions of Ihram such as cutting hair, clipping nails, wearing perfume, or having sexual intercourse.
Since sexual intercourse has taken place-as mentioned in the above question-, her Umrah is void and she is obliged to make it up immediately by offering a new Umrah when she is capable to do so.
" Having sexual intercourse while offering a single Umrah (not the one in Qiraan Hajj) renders it void……..However, if this violation was committed by a non- discerning boy, a mad person, an oblivious person, an ignorant person, or a coerced person, then their Umrah is considered valid. Nevertheless, if a discerning man has committed that violation, then he is obliged to slaughter a she-camel as an expiation."{Moghni Al-Mohtajj/Al-Khateeb Ash-Shirbini}.
If that violation was committed by a woman, then there are two opinions for the scholars as regards the obligation of offering a she-camel:
First opinion: She isn`t obliged to slaughter an animal, and this is the opinion of the Ramli, a Shafite scholar. "No ransom is due on her according to the correct opinion of the Shafite scholars, whether her husband was in a state of Ihram or not when he slept with her."{Moghni Al-Mohtajj}.
Second opinion: The wife is obliged to slaughter a she-camel in case her husband wasn`t in a state of Ihram when he slept with her; as stated by Ibn Hajjar, a Shafite scholar. Note: Badanah is a camel or a she-camel, and it should have the same age of Udhiyah(sacrifice in Eid-ul-Adha).
To be on the safe side, it is better for her to delegate someone, living in KSA, to slaughter a She-camel on her behalf and distribute its meat amongst the poor people of Makkah, then she should go back there to make up her incomplete Umrah by offering a new one as soon as possible. And Allah knows best.