Dying

Being at death door and being miraculously healed or whispering who their murderer was with one's last breath, has a long fantasy tradition. Fighting at full strength until the moment of death (zero HP), does not capture this tradition. Therefore:

At zero hit points or less the character can no longer fight with a weapon, defend or cast spells and moves at a maximum of 5’ / round by crawling along the ground. Any attack against the character is at +4 to hit and the character cannot use a shield or their dexterity bonus to defend the attack. The character can speak, use a wand or carry out some other action of minimal exertion. It is the stuff of heroes to do so!

Upon first going into negative hit points the character must immediately make a saving throw vs death ray, modified by constitution bonus, and subtracting the amount of hit points less than zero.  Twenty always succeeds: one always fails. If failed the character is dead! Roll on B/X Blackrazor's 50 ways to die table. 
I do love that on my DM screen how this table is the most prominent table that faces my players!

At the conclusion of each subsequent round the character will lose an additional 1-6 hit points and must make another saving throw vs death ray using the current negative hit points as penalty.

Only magical healing, miraculously closing mortal wounds, can save the character. Without miracle, mortal wounds in mediaeval times, were just that, mortal. So staunching the blood as per other house rules will have no effect on the outcome but may at DM discretion allow time for the character to say a final goodbye.

Magical healing, assuming it is strong enough to overcome the negative hit points, will only return the character to zero hit points. After that the character either needs further magical healing or to heal in the normal way with rest.  If the magical healing is insufficient to overcome the negative hit points, the character is still dying and will need to make a new saving throw against death at the end of the round, using the new negative hit points to modify the saving throw. Without further magical healing the character will still die.

Example: Roderick 5HP is struck for 8 HP damage and is reduced to -3 HP.  He must make an immediate saving throw vs death ray at -3 - he passes! Seana cast cure light wounds on Roderick in the next round but rolls a 1, healing only 2 hit points. At the end of this round Roderick rolls d6 to find out how many further hit points he has lost and rolls a 3, he is now -4HP. He passes his saving throw again by rolling a 20! Seana has one more cure light wounds, this time she rolls a 6, healing 7 HP. Roderick is saved but is at ZERO HP. The additional 3HP of healing are wasted.