The following is the transcription of the lecture given by Shaykh Muhammad Bazmool (hafidhahullah) :
The Fiqh Principle of Istihala – Changing from impure to pure
(Taken entirely from a dars given by Sh. Muhammad Bazmool, Professor at Umm ul Qura Makkah translated by Moosa Richardson and a fatwa given by Shaykh al-Albaani)

Istihala is when something becomes pure.  It was najis (impure) but it is now taahir (pure).  A good example would be maitah (animal carcass):  it is najis, but should it be burned and become ashes, or decompose and become earth, then it is taahir, it is no longer najis.  This can happen with dung or feces or whatever.  Whenever something changes from one property to another, then the ruling likewise changes.

Example:  Let us say that someone uses the fat of a dead animal to make soap.  That fat is najis, but the chemical change that it was put through makes it taahir.

Ibn Hazm put it concisely when he said,

"Ruling upon an object is upon what it is named (what it is), if the name (what it is) changes then so does the ruling."

He also mentioned in his book of fiqh, Al-Muhalla:  "If the quality of the substance of naturally impure objects changes the name which was given to it so that it is no more applicable to it and it is given a new name which is given to a pure object, so it is no more an impure thing.  It becomes a new object, with a new rule."

Meaning that if the natural composition of a substance changes to another substance of a different composition, so much so that you can no longer call the new substance by the name of what it was-- ruling upon that substance changes too.

Proof/Example 1:

The companions (radyallahu anhum) used to eat a cheese that came from the land of the disbelievers.  In that cheese was a part of the calf which was slaughtered by the disbelievers in a way that is not in accordance with Islaam.  The companions knew this, but they also  knew that the prohibition was upon the calf, what is directly from the calf, and what could be properly called part of the calf; the ruling is not upon that which you cannot identify as part of the calf nor is it called any longer such-and-such part of the calf.  This is called istihala.

Proof/Example 2:

Another proof from the Sunnah:  The Prophet (sallallahu 'alayhi wa sallam) forbade making vinegar out of wine, but he said that if you should come across vinegar that has been made from wine then it is halaal.  

Why?

The ruling is upon what the object is, and not what it was.  Wine is haraam; vinegar is not, and before the wine became an intoxicant, it was halaal.  Why?  Because it was fruit before that.

Proof/Example 3:

Allah says in the Qur'an:

"And surely there is a lesson for you in the cattle we give you to drink of what is in their bellies from between the feces and blood, pure milk, wholesome to those who drink it." (16:66)

Allah is putting forth an example for us of how something pure can come from something impure.

And we can also use as proof something that we've already gone over.  The Prophet (sallallahu 'alayhi wa sallam) said that when the hide of maitah (the carrion) is tanned, then it is taahir.  He (sallallahu 'alayhi wa sallam) gave us a method to purify something which was first impure.  

Let us examine things we are familiar with: mono and diglycerides, whey, gluten, emulsifiers, gelatin, and whatever else is on the international haraam list.  These by-products sometimes come from animals, pigs even, in which case the ruling on the initial substances is that they are haraam.  But the initial substances (e.g. fat, marrow, cartilage, etc.) are put through chemical change so that you no longer can even call it "pig fat" or "animal bone" or "skin" or "cartilage", etc. because it is no longer that, hence it is taahir, it is halaal.

What is gelatin?  As Oxford dictionary of science defines:  "A colorless or pale yellow, water-soluble protein obtained by boiling collagen with water and evaporating the solution.  It melts when water is added and dissolves in hot water to form a solution that sets to a gel on cooling." (page 290)

Is this a chemical change or is this not a chemical change?  Is it protein any longer?  No, it is not.

You are in disbelief so you ask, "But how can it be halaal when it came from something haraam?"

Because of the proofs mentioned above, the ruling is not based upon what it was, the ruling is based upon what it is.  A Hanafi scholar, Ibn Abedin gave the example:  "the swine which drowns in a salt lake and decomposes and becomes salt itself, is now halaal."

And other Hanafi scholars go on to say: "salt is different from meat and bones.  If they become salt, they are salt."

To take the salt example further:  salt consists of sodium chloride (NaCl) when together they are the halaal food known as salt, when separated they make up two poisonous substances which are then haraam for consumption.

The ahnaaf (Hanafis) also use as an example the human semen, saying that it is najis, then when it inseminates the egg and becomes a blood clot it is still najis, but when it becomes flesh it is no longer najis.  And the ahnaaf are not the only ones who take this position.

The examples are numerous and they extend beyond food:  Yesterday a man was kaafir and going towards Hell, today he is Muslim, so what is the ruling upon him?  It is based upon what he is today.

We must be careful when we call things haraam because it is a form of thulm (oppression) .  Scholars have said that it is worse that you make something halaal to haraam rather than making something haraam to halaal.  This deen Allah has made yusr (easy) let us not make it 'usr (hard).  Wallahu 'Alim.