Ignatius encourages us to continually pray for the needs and salvation of others.
"And pray ye without ceasing in behalf of other men. For there is in them hope of repentance that they may attain to God. See, then, that they be instructed by your works, if in no other way. Be ye meek in response to their wrath, humble in opposition to their boasting: to their blasphemies return your prayers; in contrast to their error, be ye stedfast in the faith; and for their cruelty, manifest your gentleness. While we take care not to imitate their conduct, let us be found their brethren in all true kindness; and let us seek to be followers of the Lord (who ever more unjustly treated, more destitute, more condemned?), that so no plant of the devil may be found in you, but ye may remain in all holiness and sobriety in Jesus Christ, both with respect to the flesh and spirit." (Ignatius to the Ephesians, Chapter 10)
Our posture towards those outside the church should be first to pray for them that they might find repentance. Their error may seem beyond healing to us but, as Ignatius previously taught, there is a Healer that heals. Secondly, we should live lives that are consistent with the prayers we pray. We should live lives that show the fruit of the repentance we hope for others as being active in our own lives. And finally, we should live as brothers even to the lost. To be their brothers and sisters it is not necessary that we participate with them in their sin but rather that we treat them with the kindness and compassion that brotherly love commands. We don't have to go drinking with them in the bars or curse and sewer with them at their parties to become their brethren, we merely have to show them brotherly kindness as those who were once also trapped in sin and lawlessness.
Ignatius continues to exhort us who are found in Christ to remain in Christ.
"The last times are come upon us. Let us therefore be of a reverent spirit, and fear the long-suffering of God, that it tend not to our condemnation. For let us either stand in awe of the wrath to come, or show regard for the grace which is at present displayed— one of two things. Only [in one way or another] let us be found in Christ Jesus unto the true life. Apart from Him, let nothing attract you." (Ignatius to the Ephesians, Chapter 11)
There are many things that motivate us towards God. Some days, the revelation of the grace of God is enough to keep us steadfast in Christ; to motivate us to resist sin and to stand firm even in the face of temptation. However, other days, His grace seems dim and distant, in those days its the revelation of the fear of God that keeps us in Christ. Either way, what is important is that we stand. God knows what we need in every situation, either the revelation of grace or revelation of awe and fear, and it's His love that reveals one or the other as we need to keep us in His Son and to keep us bound towards Him.
Finally, Ignatius reminds the Ephesians of their unique calling in Christ.
"I know both who I am, and to whom I write. I am a condemned man, ye have been the objects of mercy; I am subject to danger, ye are established in safety. Ye are the persons through whom those pass that are cut off for the sake of God." (Ignatius to the Ephesians, Chapter 12)
This passage is a bit enigmatic, but it seems to indicate that Ephesus was along the route that the condemned Christians of that area would take to Rome and to their deaths. Ignatius seems to congratulate them for their use of the grace and mercy of God that was upon them, that they would come and fellowship with even the condemned; to encourage them and pray for them and send them on their way to Rome with the blessings of God. What a unique calling and gift in that time and place.