Around non-mahram men
Does the Muslim woman cover her feet in front of non-mahram men? The majority of the madhabs believe so, and that is the correct opinion.
The opinion of Imam Malik, Imam Shafi'i and Imam Ahmad is that everything the woman is 'awrah in front of non-mahram men. This also means that the feet must be covered.
أخبرنا محمد بن الحسن بن هارون، قال: حدثنا محمد بن الصباح، قال: حدثنا عبد الله بن رجاء، عن ابن عجلان، عن سمي، عن أبي بكر بن عبد قال: كل شيء من المرأة عورة حتى ظفرها
أحكام النسا ص33 من ابو بكر الخلال
Abu Bakr ibn Abd al-Rahman (student of Abu Hurayrah) said:
"Everything of the woman is 'awrah, down to her nail."
[Ahkaam an-Nisaa page 33 athar 23, from Al Khallal]
The Hadith used to indicate that the feet fall under awrah is the Hadith in Sunan Tirmidhi. Umm Salamah (wife of the Prophet (ﷺ)) asked about covering the feet when she is outside.
The Prophet (ﷺ) said:
"Whoever has his garment dragged out of pride, Allah will not look at him on the Day of Resurrection."
Umm Salamah asked: “What should women do with their hems? He said: “They should lower it a hand span.” She said: But then the feet will be seen. The Prophet (ﷺ) said: “Then lower it a cubit (44 centimeters), but no more than that."
[Sunan al-Tirmidhi 1731 (Hasan Sahih)]
And then comes the question: "What if my abaya gets dirty from the ground outside?". That is exactly what the Prophet was asked about.
Umm Salamah (the wife of the Prophet (peace be upon him)) reported:
I said to the Prophet (ﷺ): "I am a woman whose clothes drag on the ground, and I may walk through a dirty place." The Messenger of Allah (ﷺ) thereupon said: "That which comes after purifies it."
[Sunan al-Tirmidhi 143 (Hasan)]
So the Abaya is purified by what comes after. One does not have to worry about the Abaya getting dirty when it is dragged over the ground. If obvious impurity appears on it, it should be removed.