Paul had come to Rome as a prisoner. While at Caesarea he exercised his right as a Roman citizen to appeal to Caesar (Acts 25:11; 28:19).
If then I am a wrongdoer and have committed anything for which I deserve to die, I do not seek to escape death. But if there is nothing to their charges against me, no one can give me up to them. I appeal to Caesar. (Act 25:11 ESV)
Only the large platform of the Basilica Julia remains in the Roman Forum. The building was not completed when it was dedicated by Julius Caesar in 46 B.C. The building burned and was reconstructed by Augustus in A.D. 12. Amanda Claridge, Rome: An Oxford Archaeological Guide, describes the Basilica Julia in the following words:
The basilica was the seat of the Court of the Hundred (the centumviri), a special civil court which generally dealt with matters of inheritance and actually numbered 180 judges when they all sat together at an important trial. Pliny the Younger describes the scene at one where he pleaded on behalf of a senatorial lady suing her 80-year-old father, who had disinherited her ten days after he took a new wife. In addition to the judges the place was packed with onlookers. Both parties had brought in large numbers of seats for their supporters, behind which were rows of people standing as far as the outer walls, and the crowd spilled upwards in the galleries, hanging over the rails in their efforts to hear the proceedings. (89-90)
Some scholars suggest that this is where Paul’s appeal before Caesar would have been heard (Wycliffe Historical Geography 545).
The information above describing the crowds that came to the court might provide some understanding of Paul’s statement to Timothy.
Do your best to come to me soon. For Demas, in love with this present world, has deserted me and gone to Thessalonica. Crescens has gone to Galatia, Titus to Dalmatia. Luke alone is with me. Get Mark and bring him with you, for he is very useful to me for ministry. Tychicus I have sent to Ephesus. When you come, bring the cloak that I left with Carpus at Troas, also the books, and above all the parchments. Alexander the coppersmith did me great harm; the Lord will repay him according to his deeds. Beware of him yourself, for he strongly opposed our message. At my first defense no one came to stand by me, but all deserted me. May it not be charged against them! But the Lord stood by me and strengthened me, so that through me the message might be fully proclaimed and all the Gentiles might hear it. So I was rescued from the lion’s mouth. The Lord will rescue me from every evil deed and bring me safely into his heavenly kingdom. To him be the glory forever and ever. Amen. (2 Timothy 4:9-18 ESV)