From Piskei Teshuvot (collected by Harav Avraham Pietrekovsky of Lodz) part 2, #164
Quoting from the Imrei David, Harav Hagaon David Halevi Horowitz zt"l of Stanislav

Though we hope tragic halakhic questions like the one that follows will never occur again, the two principles behind the response are far-reaching.

The Tragic Question
A man in Krakow became ill with typhus, a highly contagious disease. He was, thank G-d, sent a cure, but was forced to remain in the hospital for a month of recuperation. He naturally asked that his tefillin be sent to him. This simple request, however, created quite a confusion among the Torah scholars of Krakow. Because typhus is so contagious, medical policy was that upon leaving the hospital, all of the patient's possessions were to be burned. Is it permissible, they asked, to send tefillin to the recuperating patient, knowing that doing so will cause their eventual destruction?

Why Not to Send the Tefillin
A number of aggadic Talmudic passages seem to indicate that even a sin indirectly brought about by a person is identified as his.

1. King Shaul is considered responsible for killing the Givonites (Shmuel II, 21:1 -- There were three years of famine in David's time. They inquired from the Urim Vetumim about its cause, and G-d replied that it came as a result of Shaul's killing the Givonites). Actually, Shaul had the inhabitants of the Nob, the city of Kohanim killed. The Kohanim had been supplying the Givonites with food. Shaul's killing Nov's inhabitants only indirectly caused the death of the Givonites, yet he is called their murderer. (Yevamot 78b)
2. King David is considered responsible for the death of Nov the city of Kohanim, Doeig, and Shaul and his three sons! Even though David only visited Achimelech the Kohein of Nov, who gave him food and the sword taken from Goliat (Shmuel I, 21). Doeig informed Shaul that David had been to Nov and Shaul ordered the killing. Yet David is also considered responsible for their deaths. (Sanhedrin 95b)
3. A number of Amoraim considered themselves responsible for the death of Rav Ada bar Ahava, even though his death was a miraculous act of G-d. (See the long story and Tosafot's comments on Bava Batra 22a)
4. Tzidkiahu is told by the prophet "You burned this city (Jerusalem)," (Yirmiyahu 38:23) because, as Rashi explains, he was the cause of its destruction and the Babylonians actually burned it.

Similarly, sending the tefillin to the hospital knowing they will eventually be burnt is tantamount to burning them.

Why to Send the Tefillin
Despite all of the above, Rav Horowitz decided that the tefillin should be sent to the patient. Putting on tefillin is a mitzva that immediately obligates the man and their burning is a future possible -- even probable, even certain -- event. It is our mandate to do the mitzvot we are obligated in at the moment despite possible future negative repurcussions. There are two precedents for this:

1. King Chizkiyahu refrained from having children because he saw through mystical insight that his son would be the wicked Menasheh. He was told by the prophet Yeshayahu, "The secrets of the All Merciful One are none of your business." You are obligated to "Be fruitful and multiply," even though you correctly know that the son will turn out wicked.
2. Amram, when he heard of Pharaoh's decree to throw all of the male children into the Nile, separated from his wife and all of the Jewish men followed suit. Why bring children into the world, only to have them murdered by the Egyptians? This position was, as his daughter Miriam pointed out, incorrect. Their obligation was to "Be fruitful and multiply," even though it would indirectly bring about the death of their sons at the hands of the Egyptians.

Similarly, the mitzva of tefillin should be kept as commanded, regardless of the seemingly sure tefillin burning that would follow.

Other Voices
Rav Horowitz points out that the Gaon of Dvinsk argues and takes the stringent position, not to send the tefillin. He sticks to his own, though, and advises sending them and hoping for the best.