Convict stowaways crossing the Pacific in 1796

A paper from 1923 called The Odyssey of Thomas Muir (Marjorie Masson and J. F. Jameson) describes the episode. Among the people forced ashore, one died, one escaped to Guayaquil, a few stayed in Mexico and a few were sent on to Havana. NB, If anyone can yet show what happened to those last people sent towards Spain, I will accept their answer over this one.

Muir was "transported" to Australia after being convicted in Edinburgh of circulating the work of Thomas Paine. Port Jackson is Sydney Harbour, where Dorr let Muir and two servants board clandestinely. A handful of others also managed to get on board with less intrigue. When the Otter and Sutil met in Nootka, Captain Dorr, with uncomfortably many people aboard, gave Captain Tovar five sailors in exchange for provisions, and Muir also got onto the Sutil.

Both ships stopped separately in California. Muir had a nice visit with Governor Borica and continued to San Blas, where Tovar was arrested and dismissed for bringing him. Muir lost an eye when the ship bringing him to Cadiz was attacked by a British squadron. Still a political case, Muir died in poverty in Paris.

Borica sold Dorr provisions but would not let him disembark anyone. Then, on subsequent nights, Dorr put ashore five and six people at gunpoint:

Of the eleven, three were of the original crew, Andrew Lambert, carpenter, and his apprentice, of Boston, and a wig-maker from London. One was a Briton marooned at Nootka by his captain. The rest are reported as stowaways from Botany Bay, two of them sailors, one a carpenter, one a tailor, two blacksmiths, one of whom was a Philadelphia negro. The rest were from London, Liverpool, and Lincoln. The woman, Jane Lambert, of London, admitted that she was a transported convict, though in later testimony she constantly maintained that she was married to Andrew Lambert in Boston years before and had a daughter of thirteen living there in the care of grandparents. But as her age on this first mention is given as twenty-seven, and Lambert's as twenty-five, we are under no obligation to believe her.

Borica put his guests to work, at smithwork and carpentry, until finally, nearly a year later, he found a chance to send them to San Blas, where they arrived late in November, 1797. Then the papers, multiplied in the usual tedious manner of Spanish officials, and now reposing in the Mexican archives, show them journeying up to Mexico and from there to Vera Cruz, whence in July, 1798, most of the are sent off to Havana. One had died, one had escaped as a stowaway on a galleon to Guayaquil. Andrew and Jane Lambert manifesting a willingness to become Catholics, and Peter Pritchard of Liverpool already such, are encouraged to remain; but while Andrew Lambert works steadily at his trade as a ship carpenter in Vera Cruz, Jane is a source of much trouble to the authorities, falling into habits of intemperance, and going away, for a cure apparently, and residing in the house of Don Juan Oquelli (O'Kelly) in Mexico and of Don Tomas Murphy in Jalapa, much respected citizens, who look out for her as well as they can. It is an interesting picture of humble life in Mexico at the time-the affectionate but illiterate letters which Lambert sends after her, written for him by a Spanish lady of much kindness but little orthography; the English-speaking Father Nicolas Arsdequi (Archdeacon) who received them into the church; the details of their finances, their journeyings, their progress in the catechism. But what most impresses one in their story is, as in the case of Muir, the ceaseless and minute vigilance with which the whole administration of New Spain, from the viceroy down, kept its eye upon all the doings of every foreigner, and struggled to preserve state and church from contaminating influences.

I found this entry on the website of the Australian National University,which tells the interesting story of Thomas Muir, a dissident we might call him today of the United Kingdom.

Entry on Thomas Muir

Sentenced to Transportation, he settled in Sydney. This is where the Otter arrived and he indeed planned his escape, but not only was he not a stowaway, he travelled in collusion with her captain, Ebenezer Dorr.

Urged by his companions Muir planned his escape with Dorr. On the night of 17 February he made his way out of the harbour in a small boat with two servants and was picked up by the Otter some miles off the coast.

He made it to the New World but

After crossing the Pacific and reaching Nootka Sound, he learned that H.M.S. Providence was then in those waters. Fearing recapture, he transferred to the Spanish gunboat Sutil and in June 1796 reached Monterey, Spanish California, where he was hospitably received by the governor.

After a tragic series of events he ended up severely injured and maimed, made it to Spain and then France, where he died in poverty and obscurity.

As the gist of your question is about this eventual fate, I'll quote it in full,from the website

Under the covert surveillance of the Spanish authorities he was allowed to go by sea to San Blas and thence by land to Mexico City and Vera Cruz. In November 1796 he reached Havana, but owing to the outbreak of war between England and Spain he was imprisoned there for four months and his original intention of reaching Philadelphia was frustrated. He was placed on board the frigate Ninfa sailing for Spain, but close to her destination she was intercepted by a British squadron under Sir John Jervis. In the subsequent engagement Muir was severely wounded in the face and lost his left eye, and though the British learnt he was on board they failed to recognize him because of his mutilation. He was sent ashore with the Spanish wounded to the hospital at Cadiz, whence news of his plight reached Paris; after some months he was released through the intercession of Talleyrand, the French foreign minister, and in December 1797 reached Paris. Here he was for a time a guest of the Directory and was consulted on proposals for an invasion of England, while the circumstances of his exile, wounds and disfigurement centred much public attention upon him. In two quarto volumes he prepared a manuscript, since lost, describing his exile and travels, and offered it to the French government as security for a small estate to which he could retire and recruit his shattered health. For months his petition remained unheeded; neglected by friends, pursued by poverty and enfeebled by his wounds, he drifted into obscurity. He died at Chantilly, near Paris, on 26 January 1799. His burial place is unknown.