It is unclear what became of Joseph Bullock, Pitt's manager and all-around man of business, after Pitt's death in 1806. It does seem, however, that he worked for some time at the Royal Menagerie. However, by the beginning of 1814, Bullock found himself in a difficult situation with the Treasury. He clearly found recourse to appeal to Mary, the Countess of Chatham, who was Pitt's sister in-law, for assistance in his difficulties.
On January 12th, 1814, Mary Elizabeth Chatham wrote to Lady Liverpool about Bullock's situation:
“My dear Ly. Liverpool,
A few more last words about poor Bullock I must plague you with, but, they shall be very few of mine at least. - I will refer you to his Letter which I enclose, & to the Copy of ye Ins. [instructions?] he has sent to the Treasury.
I must confess I had been astonished at the Statement in the Document you sent me, & so I rather think I let you see I was. - I have such perfect confidence in Bullock’s veracity, as well as in his accuracy & clear habitualness as a man of business, that I would not easily believe his having been in a gross Error as it appeared from that paper.
However, there is is again before the Treasury, & I can only say that I shd. be dissatisfied with myself if I left anything untried on my part in his Course, & that I am most extremely obliged to you for the part you have taken in it. - & as you will see by his Letter, is bad. - Forgive me, dear Ly. Liverpool, for being much a bore, & believe me, Yrs. most truly, M.E. Chatham
Jany. 12th 1814.” 
The day before, Joseph Bullock had written to ‘Madam’ (Lady Chatham) from the Royal Menagerie:
With a very grateful heart I do most humbly acknowledge the great condescension with which your Ladyship has been pleased to interest yourself in my behalf, and Madam I beg to express my deep regret at not having been able from the complicated nature of my case to avail myself of your goodness without giving you the trouble of repeated applications. -
Until your Ladyship transmitted to me the Document which accompanied your note I had failed in obtaining anything like an explicit answer from either W. Wharton or W. Harrison; and had the Document in question been sent to me by them previous to my last trespass upon your attention I should not have felt myself driven to it but should of course have returned my Answer to the Lord’s Commissioners as you now receive it, and as I have transmitted it to their Lordships.
Nothing but the deep grief that I feel at having been represented in “The Memorandum” as pleading for a restoration of my property on false pretensions, could have induced me to address you again upon the Subject, for what, Madam, must be the natural inference, if my plea had been so constituted, than that I was indifferent to the benignant intentions of W. Pitt towards me, that I was making in a thankless spirit of discontent a causeless complaint of losses which did not exist and that I was ungratefully abusing the condescending goodness of both my Lord and yourself? -
To the Countess of Liverpool, Madam, for the notice which she has taken of my application at your Ladyship’s expression, I feel most sensibly my obligation, and it is my bounden duty to mention it with gratitude which I would fain [sic] hope that were the Circumstances which my Answer to this Memorandum comprehends known to her Ladyship, my appeal would not appear to her to have been without its apology, and perhaps I may add, its justification.
Since your Ladyship sent the Memorandum I have received from W. Harrison a letter in which he says that “Their Lordships can see no ground for complying with my applications” either as they respect the Warrant or my sacrifice of property in maintaining the Animals for eleven years and a quarter in such supply as the inadequate allowance during that time rendered indispensable and without which they must have starved. -
This letter I have answered by informing W. Harrison that “I have transmitted to their Lordship’s and Answer to the Memorandum which had reached me.” -
I am Madam,
Your Ladyship’s most grateful and most humbly obedient servant,
Joseph Bullock.” 
Mary, the Countess of Chatham, had enclosed Bullock's letter to her with her own short note to Lady Liverpool. It is clear from internal evidence in Bullock's note that he was the very same man who worked for William Pitt. What became of him after his debacle is not known, however Lady Chatham was very kind in forwarding his case with Lady Liverpool as she remembered Bullock's good character during his time in Pitt's employ.
1. The Liverpool Papers. British Library, Add Ms 38255, Vol. LXVI, ff. 354-5.
2.The Liverpool Papers. British Library, Add Ms 38255, Vol. LXVI, ff. 356-7.