Firstly, Islam and Christianity have different definitions of "Martyr;" it is entirely wrong to liken someone like St. Ignatius, who was fed to lions, to an Islamic terrorist.
Roman control varied in different parts of the Empire; even Diocletian was unable to fully exterminate the Church. Several Emperors beginning with Trajan did not actively hunt for Christians and indeed discouraged such persecution.
Now, further to the point, regarding the Pauline epistles, or indeed the epistles of other Apostles or early bishops like St. Ignatius (who was fed to lions), the question as to how these were transmitted or survived becomes less compelling when one considers the difficulty our contemporary governments have monitoring communications, with all their technology. Rome had only the most primitive cryptography (the Caesar Cipher and related schemes) and no effective surveillance; when one lacks electrical lighting, let alone infrared night vision, monitoring what people do at night becomes rather difficult, and early Christians typically worshipped before dawn (Matins) and after dark (Vespers). Even today one can visit Orthodox monasteries where the main liturgy starts at midnight.
There were dramatic persecutions however, and it is not unreasonable to assume that more was lost than was preserved.
Now, did the Roman Empire under St. Constantine manage to edit, control or otherwise censor the surviving material? This charge is sometimes raised by some Protestants. However, before the conversion of the Roman Empire, Christianity had spread substantially beyond its borders, to Edessa, across Syria, the Persian Empire, and into India, and into Armenia.
The Nestorians took refuge in the Persian Empire after Ephesus, which shows that these regions could become havens for dissent. Indeed the Paulicians dwelt in Armenia for over a thousand years.
Yet, in all of these varied regions, the contents of the NT were essentially uncontroversial. The Ethiopians bundled into their NY the Didascalia and a few other items in addition to the Athanasian canon, and the Syriac Aramaic Peshitta lacked some of the epistles. However, there was never any real controversy over this.
Tatian, in the second century, did compose a harmony of the four Gospels known as the Diatessaron, however, he was a bit Gnostic, and this rather unsatisfactory work was replaced by the Peshitta in the course of the fourth century.
Interestingly a large number of Gnostic texts entirely repudiated by the Nicene Church did survive and have emerged in recent years, for example, at Nag Hammadi.
You and I both know that UBL was not martyred, not even according to the most creative and novel use of the word.
