There is much to learn about sin and leprosy in the Bible. Leprosy is often associated with sin in the Bible. And though (Lev. 13) describes the identification of leprosy in a person or in their clothes, (Lev. 14) goes on to describe the lepers cleansing once, or if, he is healed. (Lev. 14:3)
And in reading through (Lev. 14), I find no place where an individual's sin is mentioned as the cause of the leprosy. Yet part of the cleansing process has to do with the offering and killing of sacrifices. (Lev. 14:4-7) (Lev. 14:10) And it is specifically stated that some of these are for a trespass and sin offering. (Lev. 14:12) (Lev. 14:19) And, that these offerings are to make atonement for the one in question. (Lev. 14:31)
It is as though leprosy is to be identified as sin. And the leper must dwell alone without, or outside, the camp. (Lev. 13:46) Why? In order to maintain cleanliness within the camp. (Lev. 14:57) In order to remove sin outside the camp. (Ex. 29:14)
But, in all these sacrifices the blood, which is for the atonement, was kept within the camp and applied to the Tabernacle or Temple. (Ex. 29:12-13). Only the flesh and dung and skin were burnt outside the camp. (Ex. 29:14) Atonement is made for the people's sins, sin is cast outside the camp, and the camp is clean and holy. Sanctified.
Yet, at times, it is the camp that is unclean and sinful. During Moses stay in the Mountain, receiving the Law from God, the camp turned to idolatry and sinful living. (Ex. 32:1-6) Result? Moses moved the temporary tabernacle tent, which was the place of meeting until the Tabernacle proper was built, outside the camp. (Ex. 33:7) The camp was supposed to be clean and holy. Outside the camp was the place of sin and defilement. But the camp is now the place of sin and defilement. And outside the camp is where God would make his presence known and where He meets. (Ex. 33:9-11)
The writer of (Hebrews), Paul, knows his audience. Jews. They are familiar with 'outside the camp'. Paul in (Heb. 13:13) is encouraging these Christian Jews to not go back to the camp which is unclean. Cleanliness and holiness is now found outside the camp. God, and Christ are found outside the camp.
In other words, God was no longer found in Israel. He was, and still is to this day, outside of Israel. That will change one day, of course. But as of now, it is still true.
Can application be made to the church of our day? I believe it can. (Rev. 3:20) Christ is on the outside of the church beckoning those that can hear to open the door. Just as Israel became unclean and defiled, so too will/has the church, as represented in the world.
My opinion
Lees