Fair Value of Financial Instruments - Carrying Values and Estimated Fair Values of Financial Instruments (Details) - USD ($) $ in Thousands		Sep. 30, 2023	Dec. 31, 2022	Dec. 31, 2021
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Available-for-sale debt securities, at fair value		$ 2,589,000	$ 2,495,456
Fixed-maturity security held to maturity, fair value		1,285,369	1,340,265
Equity securities		29,123	35,404
Separate account assets		2,183,435	2,305,717
Surplus note		1,417,056	1,444,469
Separate account liabilities		2,183,435	2,305,717	$ 2,799,992
Fixed-maturity security (held-to-maturity)		1,417,460	1,444,920
Reported Value Measurement [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Available-for-sale debt securities, at fair value		2,589,000	2,495,456
Short-term investments (available-for-sale)		20,051	69,406
Equity securities		29,123	35,404
Trading securities		18,160	3,698
Separate account assets		2,183,435	2,305,717
Separate account liabilities		2,183,435	2,305,717
Reported Value Measurement [Member] | Level 3 [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Policy loans	[1]	37,879	35,940
Surplus note	[1],[2]	1,417,056	1,444,469
Fixed-maturity security (held-to-maturity)	[1]	1,417,460	1,444,920
Reported Value Measurement [Member] | Level 3 [Member] | Deposits [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Deposit asset underlying 10% coinsurance agreement	[1]	196,553	224,371
Reported Value Measurement [Member] | Level 2 [Member] | Senior Notes [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Notes payable - Long term	[2],[3]	593,508	592,905
Estimate of Fair Value Measurement [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Available-for-sale debt securities, at fair value		2,589,000	2,495,456
Short-term investments (available-for-sale)		20,051	69,406
Equity securities		29,123	35,404
Trading securities		18,160	3,698
Separate account assets		2,183,435	2,305,717
Separate account liabilities		2,183,435	2,305,717
Estimate of Fair Value Measurement [Member] | Level 3 [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Fixed-maturity security held to maturity, fair value	[1]	1,285,369	1,340,265
Policy loans	[1]	37,879	35,940
Surplus note	[1],[2]	1,280,803	1,333,047
Estimate of Fair Value Measurement [Member] | Level 3 [Member] | Deposits [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Deposit asset underlying 10% coinsurance agreement	[1]	196,553	224,371
Estimate of Fair Value Measurement [Member] | Level 2 [Member] | Senior Notes [Member]
Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]
Notes payable - Long term	[2],[3]	$ 473,906	$ 491,753

[1] Classified as a Level 3 fair value measurement.

[2] Carrying value amounts shown are net of unamortized issuance costs

[3] Classified as a Level 2 fair value measurement.